{"id":15704,"date":"2023-12-18T10:51:19","date_gmt":"2023-12-18T05:21:19","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=15704"},"modified":"2023-12-19T09:42:02","modified_gmt":"2023-12-19T04:12:02","slug":"envision-math-common-core-grade-6-answer-key-topic-7","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-6-answer-key-topic-7\/","title":{"rendered":"Envision Math Common Core Grade 6 Answer Key Topic 7 Solve Area, Surface Area, And Volume Problems"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 6 Answer Key<\/a>\u00a0Topic 7 Solve Area, Surface Area, And Volume Problems<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

Envision Math Common Core 6th Grade Answers Key Topic 7 Solve Area, Surface Area, And Volume Problems<\/h2>\n

Topic 7 Essential Question<\/h3>\n

How can the areas of certain shapes be found? What are the meanings of surface area and volume and how can surface area and volume be found?<\/p>\n

3-ACT MATH<\/strong><\/p>\n

\"Envision
\nThat’s a Wrap
\nThat’s a Wrap How you wrap a gift can say a lot about you. Some people conserve resources by reusing paper bags instead of purchasing wrapping paper. It may not look as nice at first, but you can unleash your crafty side and decorate the gift yourself.
\nNo matter what you use to wrap a gift, you always need to consider the size of the object and how much paper you’ll need. Think about this during the 3-Act Mathematical Modeling lesson.
\n\"Envision<\/p>\n

Topic 7 enVision STEM Project<\/h3>\n

Did You Know?
\nFood packaging is designed to identify products and to attract customers. Packaging also ensures food remains fresh and free from damage and contamination.
\n\"Envision<\/p>\n

Common types of material used for packaging are paper, cardboard, glass, steel, and aluminum. The best material to use for packaging depends on the contents\u2014for example, soup in a paper bag could be rather messy!
\n\"Envision<\/p>\n

Manufacturers consider several factors when designing packaging, such as cost, amount of material used, and potential environmental impact. Steel food cans are the most recycled food package in the United States.
\n\"Envision<\/p>\n

Packaging engineers consistently look for ways to innovate. Some food packaging is now selfopening, self-closing, or selfheating. Some packaging is biodegradable. Other advances include edible packaging.
\n\"Envision<\/p>\n

Your Task: Pack It
\nFood packaging engineers consider many elements related to both form and function when designing packaging. How do engineers make decisions about package designs as they consider constraints, such as limited dimensions or materials? You and your classmates will use the engineering design process to explore and propose food packaging that satisfies certain criteria.
\n\"Envision<\/p>\n

Topic 7 Get Ready!<\/h3>\n

Review What You Know!<\/strong><\/p>\n

Vocabulary<\/strong>
\nChoose the best term from the box to complete each definition.<\/p>\n

    \n
  • area<\/li>\n
  • parallelogram<\/li>\n
  • perpendicular<\/li>\n
  • polygon<\/li>\n
  • volume<\/li>\n<\/ul>\n

    Question 1.
    \nA triangle is an example of a three-sided ___________<\/p>\n

    Answer:
    \nA triangle is an example of a three-sided polygon.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA triangle is an example of a three-sided polygon.
    \nfor example:
    \nequilateral triangle: all the sides are equal lengths, and all the internal angles are 60 degrees.
    \nso a triangle is an example of a three-sided polygon.<\/p>\n

    Question 2.
    \n________ lines form a right angle.<\/p>\n

    Answer:
    \nPerpendicular lines form a right angle.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nperpendicular lines form a right angle.
    \nfor example:
    \ntwo lines that intersect and form right angles are called perpendicular lines.<\/p>\n

    Question 3.
    \n__________ is the number of cubic units needed to fill a solid figure.<\/p>\n

    Answer:
    \nVolume is the number of cubic units needed to fill a solid figure.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nVolume is the number of cubic units needed to fill a solid figure.
    \nfor example:
    \nA plane figure is a two-dimensional figure.
    \nso volume is the number of cubic units needed to fill a solid figure.<\/p>\n

    \"Solve<\/p>\n

    Question 4.
    \n__________ as opposite sides that are parallel and the same length.<\/p>\n

    Answer:
    \nA parallelogram as opposite sides that are parallel and the same length.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA parallelogram has opposite sides that are parallel and the same length.
    \nfor example:
    \nA rhombus is a parallelogram with sides that are all equal length.<\/p>\n

    Evaluate Expressions<\/strong><\/p>\n

    Find the value of each expression when a = 12, b = 3, c = 4, and d = 9.
    \nQuestion 5.
    \nac<\/p>\n

    Answer:
    \nac = 48.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \na = 12, b = 3, c = 4, and d = 9.
    \nac = 12 x 4.
    \nac = 48.<\/p>\n

    Question 6.
    \n\\(\\frac{1}{2}\\)b<\/p>\n

    Answer:
    \n3\/2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \na = 12, b = 3, c = 4, and d = 9.
    \n(1\/2)b.
    \n1\/2 x 3.
    \n3\/2.<\/p>\n

    Question 7.
    \nabd<\/p>\n

    Answer:
    \nabd = 324.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \na = 12, b = 3, c = 4, and d = 9.
    \nabd = 12 x 3 x 9.
    \nabd = 36 x 9.
    \nabd = 324.<\/p>\n

    Question 8.
    \n0.5a<\/p>\n

    Answer:
    \n6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \na = 12, b = 3, c = 4, and d = 9.
    \n0.5a = 0.5 x 12.
    \n0.5a = 6.<\/p>\n

    Question 9.
    \n\\(\\frac{3}{4}\\)(ad)<\/p>\n

    Answer:
    \n81.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \na = 12, b = 3, c = 4, and d = 9.
    \n(3\/4)ad.
    \n3\/4 x 12 x 9.
    \n3 x 3 x 9.
    \n9 x 9 = 81.<\/p>\n

    Question 10.
    \nab + cd<\/p>\n

    Answer:
    \nab + cd = 72.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \na = 12, b = 3, c = 4, and d = 9.
    \nab + cd.
    \n12 x 3 + 4 x 9.
    \n36 + 36.
    \n72.<\/p>\n

    Multiplication<\/strong><\/p>\n

    Find each product.
    \nQuestion 11.
    \n3.14 \u00d7 12<\/p>\n

    Answer:
    \n3.14 x 12 = 37.68.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 3.14 and 12.
    \nfind the product.
    \n3.14 x 12.
    \n37.68.<\/p>\n

    Question 12.
    \n45.8 \u00d7 5<\/p>\n

    Answer:
    \n45.8 x 5 = 229.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 45.8 and 5.
    \nfind the product.
    \n45.8 x 5.
    \n229.<\/p>\n

    Question 13.
    \n0.8 \u00d7 2.7<\/p>\n

    Answer:
    \n2.16.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 0.8 and 2.7.
    \nfind the product.
    \n0.8 x 2.7.
    \n2.16.<\/p>\n

    Question 14.
    \n14 \u00d7 7.25 \u00d7 2.5<\/p>\n

    Answer:
    \n14 x 7.25 x 2.5 = 253.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 14, 7.25, and 2.5.
    \nfind the product.
    \n14 x 7.25 x 2.5.
    \n101.5 x 2.5.
    \n253.75.<\/p>\n

    Question 15.
    \n1\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{4}\\)<\/p>\n

    Answer:
    \n0.375.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 3\/2 and 1\/4.
    \nfind the product.
    \n3\/2 x 1\/4.
    \n1.5 x 0.25.
    \n0.375.<\/p>\n

    Question 16.
    \n2\\(\\frac{1}{3}\\) \u00d7 2\\(\\frac{1}{4}\\) \u00d7 1\\(\\frac{3}{8}\\)<\/p>\n

    Answer:
    \n7.115.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 7\/3, 9\/4, and 11\/8.
    \nfind the product.
    \n7\/3 x 9\/4 x 11\/8.
    \n2.3 x 2.25 x 1.375.
    \n5.175 x 1.375.
    \n7.115.<\/p>\n

    Geometry<\/strong><\/p>\n

    Question 17.
    \nHow are parallelograms and rectangles similar and how are they different?<\/p>\n

    Answer:
    \nThe main difference between them is that a parallelogram has opposite sides that are equal.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe main difference between them is that a parallelogram has opposite sides equal.
    \nwhile in a rectangle, the opposite sides are equal with all its adjacent sides being perpendicular to each.<\/p>\n

    \"Solve<\/p>\n

    Question 18.
    \nHow are the formulas for the area of a rectangle and the area of a triangle alike and different? Explain.<\/p>\n

    Answer:
    \nArea of the rectangle = l x b.
    \narea of the triangle = 1\/2 x b x h.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the rectangle = l x b.
    \nwhere l = length and b = breadth.
    \nthe area of the triangle = 1\/2 x b x h.
    \nwhere b = base.
    \nh = perpendicular height.<\/p>\n

    Language Development<\/strong>
    \nUse the graphic organizer to help relate new vocabulary in this topic to terms you studied in previous topics.
    \n\"Envision
    \n\"Envision<\/p>\n

    Pick A Project<\/strong><\/p>\n

    PROJECT 7A
    \nIf you could pick the shape of a building to live in, what shape would it be?
    \nPROJECT: COMPARE CUBE-SHAPED BUILDINGS
    \n\"Envision<\/p>\n

    PROJECT 7B
    \nWhat are some ways you can use number cubes?
    \nPROJECT: DRAW NETS OF NUMBER CUBES
    \n\"Envision<\/p>\n

    PROJECT 7C
    \nHow far do you think a roll of wrapping paper reaches?
    \nPROJECT: CALCULATE THE AMOUNT OF GIFT WRAP
    \n\"Envision<\/p>\n

    PROJECT 7D
    \nWhat sorts of music do you like?
    \nPROJECT: WRITE A RAP BATTLE
    \n\"Envision<\/p>\n

    Lesson 7.1 Find Areas of Parallelograms and Rhombuses<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nSof\u00eda drew the grid below and plotted the points A, B, C, and D. Connect point A to B, B to C, C to D, and D to A. Then find the area of the shape and explain how you found it. Using the same grid, move points B and C four units to the right. Connect the points to make a new parallelogram ABCD. What is the area of this shape?<\/p>\n

    I can… use what I know about areas of rectangles to find the areas of parallelograms and rhombuses.
    \n\"Envision<\/p>\n

    Look for Relationships
    \nWhat relationships do you see between rectangles and parallelograms?<\/p>\n

    Focus on math practices
    \nGeneralize How can you find the area of any parallelogram?<\/p>\n

    Answer:
    \nArea of the parallelogram = b x h.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the parallelogram = base x height.
    \narea of the parallelogram = b x h.<\/p>\n

    Essential Question<\/strong>
    \nHow can you use the area formula of a rectangle to find the area formula of a parallelogram?<\/p>\n

    Try It!<\/strong><\/p>\n

    Find the area of the parallelogram.
    \n\"Envision
    \nThe area of the parallelogram is ________ cm2<\/sup>.<\/p>\n

    Answer:
    \nThe area of the parallelogram = 31.5 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the parallelogram = b x h.
    \narea = 7 cm x 4.5 cm.
    \nwhere b = base and h = height.
    \narea = 31.5 sq cm.<\/p>\n

    Convince Me! Compare the area of this parallelogram to the area of a rectangle with a length of 7 cm and a width of 4.5 cm. Explain.<\/p>\n

    Answer:
    \nArea = 15.75 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the rectangle = 1\/2( b x h).
    \narea =1\/2( 7 cm x 4.5 cm).
    \narea = 1\/2(31.5).
    \narea = 15.75.<\/p>\n

    Try It!<\/strong><\/p>\n

    a. Find the area of the rhombus.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the rhombus = 21.25.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the rhombus = pq\/2.
    \narea = 22.5 + 20\/2.
    \narea = 42.5\/2.
    \narea = 21.25.<\/p>\n

    b. The area of the parallelogram is 65 ft2<\/sup>. What is its height?
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the parallelogram = 5 ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea = 65 sq ft.
    \narea = b x h.
    \n65 = 13 x h.
    \nh = 65\/13.
    \nh = 5.
    \nso the area of the parallelogram = 5 ft.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can decompose a parallelogram and compose a rectangle to find the area of a parallelogram or a rhombus. The formula for the area of a rectangle, A = l \u00d7 w, can be written as the formula A = b \u00d7 h to find the area of a parallelogram or the area of a rhombus.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you use the area formula of a rectangle to find the area formula of a parallelogram?<\/p>\n

    Answer:
    \nThe area of the rectangle = 30 sq ft.
    \nThe area of the parallelogram = 30 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the rectangle = l x w.
    \narea = length x width.
    \nfor example:
    \narea = 6 ft x 5 ft.
    \narea = 30 sq ft.
    \nthe area of the parallelogram = b x h.
    \narea = 6 ft x 5 ft.
    \narea = 30 sq ft.<\/p>\n

    Question 2.
    \nKen combined a triangle and a trapezoid to make a parallelogram. If the area of the triangle is 12 in.2<\/sup> and the area of the trapezoid is 24 in.2<\/sup>, what is the area of the parallelogram? Explain.<\/p>\n

    Answer:
    \nThe area of the parallelogram =<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKen combined a triangle and a trapezoid to make a parallelogram.
    \nIf the area of the triangle is 12 in.2and the area of the trapezoid is 24 in.2.
    \n<\/sup>area of the parallelogram = b x h.
    \narea = 12 x 24.
    \narea = 288 sq in.
    \nso the area of the parallelogram = 288 sq in.<\/p>\n

    Question 3.
    \nCritique Reasoning A parallelogram is 3 meters long and 7 meters high. Liam said that the parallelogram’s area is greater than the area of a rectangle with the same dimensions. Is he correct? Explain.<\/p>\n

    Answer:
    \nYes, he was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA parallelogram is 3 meters long and 7 meters high.
    \narea of the parallelogram = b x h.
    \narea = 7 x 3.
    \narea = 21.
    \nso he was correct.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 4-6, use a formula to find the area.
    \nQuestion 4.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the parallelogram = 430.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the parallelogram = b x h.
    \narea = 20 x 21.5.
    \narea = 430.
    \nso the area of the parallelogram = 430.<\/p>\n

    Question 5.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the parallelogram = 200.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the parallelogram = b x h.
    \narea = 16 x 12.5.
    \narea = 200.
    \nso the area of the parallelogram = 200.<\/p>\n

    Question 6.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the parallelogram = 120.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the parallelogram = b x h.
    \narea = 12 x 10.
    \narea = 120.
    \nso the area of the parallelogram = 120.<\/p>\n

    Question 7.
    \nA rhombus has an area of 440 m2<\/sup> and a base of 22 m. What is its height?<\/p>\n

    Answer:
    \nThe diagonal of the rhombus = 40.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA rhombus has an area of 440 sq m and a base of 22 m.
    \narea of the rhombus = pq\/2.
    \nwhere p = diagonal and q = diagonal.
    \narea = pq\/2.
    \n440 = px 22\/2.
    \n440 = 11p.
    \np = 440\/11.
    \np = 40.<\/p>\n

    \"Solve<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 8\u201311, find the area of each parallelogram or rhombus.
    \nQuestion 8.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the parallelogram = 12 sq yd.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the quadrilateral = b x h.
    \nwhere b = base and h = height.
    \narea = 2 x 6.
    \narea = 12 sq yd.<\/p>\n

    Question 9.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 24 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the parallelogram = b x h.
    \nwhere b = base and h = height.
    \narea = 6 x 4.
    \narea = 24 sq m.<\/p>\n

    Question 10.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the rhombus = 52.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the rhombus = pq\/2.
    \nwhere p = diagonal and q = diagonal.
    \narea = pq\/2.
    \narea = 10.5 x 10 \/2.
    \narea = 52.5.<\/p>\n

    Question 11.
    \n\"Envision
    \nAnswer:
    \nArea = 20.7 sq yd.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the parallelogram = b x h.
    \nwhere b = base and h = height.
    \narea = 9 x 7\/3.
    \narea = 9 x 2.3.
    \narea = 20.7 sq yd.<\/p>\n

    Question 12.
    \nThe area of the parallelogram is 132 in.2<\/sup>. What is the height of the parallelogram?
    \n\"Envision<\/p>\n

    Answer:
    \nheight = 12 in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the parallelogram = b x h.
    \nwhere b = base and h = height.
    \n132 = 11 x h.
    \nh = 12\u00a0 in.<\/p>\n

    Question 13.
    \nThe area of the rhombus is 52 m2<\/sup> What is the base of the rhombus?
    \n\"Envision<\/p>\n

    Answer:
    \nThe diagonal of the rhombus = 16.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA rhombus has an area of 52 sq m and a base of 6.5 m.
    \narea of the rhombus = pq\/2.
    \nwhere p = diagonal and q = diagonal.
    \narea = pq\/2.
    \n52 = px 6.5\/2.
    \n52 = 3.25p.
    \np = 52\/3.25.
    \np = 16.<\/p>\n

    Question 14.
    \nMicah and Jason made parallelogram-shaped stained glass windows with the same area. The height of Micah’s window is 9 inches, and its base is 10 inches. The height of Jason’s window is 6 inches. What is the base of Jason’s window?
    \n\"Envision<\/p>\n

    Answer:
    \nThe base of Jason’s window = 15 in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMicah and Jason made parallelogram-shaped stained glass windows with the same area.
    \nThe height of Micah’s window is 9 inches, and its base is 10 inches.
    \nThe height of Jason’s window is 6 inches.
    \narea = b x h.
    \n90 = b x 6.
    \nb = 90\/6.
    \nb = 15.
    \nso the base of Jason’s window = 15 in.<\/p>\n

    Question 15.
    \nA rectangle has a length of 8 m and a width of 4.5 m. A parallelogram has a length of 6 m. The area of the parallelogram is twice the area of the rectangle. What is the height of the parallelogram?<\/p>\n

    Answer:
    \nThe height of the parallelogram = 3m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA rectangle has a length of 8 m and a width of 4.5 m.
    \nA parallelogram has a length of 6 m.
    \narea of rectangle = 8 x 4.5.
    \narea = 36.
    \narea of parallelogram = 6 x h.
    \n18 = 6 x h.
    \nh = 18\/6.
    \nh = 3.<\/p>\n

    In 16 and 17, use the picture at the right.
    \n\"Envision
    \nQuestion 16.
    \nHilary made an origami dog. What is the area of the parallelogram that is highlighted in the origami figure?<\/p>\n

    Answer:
    \nThe area of the parallelogram = 9.44 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the parallelogram = b x h.
    \narea = 4 cm x 2.36 cm.
    \nb = base and h = height.
    \narea = 9.44 sq cm.<\/p>\n

    Question 17.
    \nA type of origami paper comes in 15 cm by 15 cm square sheets. Hilary used two sheets to make the origami dog. What is the total area of the origami paper that Hilary used to make the dog?<\/p>\n

    Answer:
    \nThe total area of the origami papaer = 225 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA type of origami paper comes in 15 cm by 15 cm square sheets.
    \nHilary used two sheets to make the origami dog.
    \nthe total area of the origami paper = 15 x 15.
    \narea = 225 sq cm.
    \nso the total area of the origami paper = 225 sq cm.<\/p>\n

    Question 18.
    \nReasoning A rectangle and a parallelogram have the same base and the same height. How are their areas related? Provide an example to justify your answer.<\/p>\n

    Answer:
    \narea = 1\/2 x bh.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA rectangle and a parallelogram have the same base and the same height.
    \narea of the rectangle = 1\/2 b x h.
    \narea = half of the base x height.
    \narea of the parallelogram = l x w.
    \nwhere l = length and w = weight.<\/p>\n

    Question 19.
    \nSoshi’s rhombus has a base of 12 in. and a height of 10 in. Jack’s rhombus has base and height measures that are double those of Soshi’s rhombus. Compare the area of Jack’s rhombus to the area of Soshi’s rhombus. Explain.<\/p>\n

    Answer:
    \nThe area of Jack’s rhombus to the area of Soshi’s rhombus = 120.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSoshi’s rhombus has a base of 12 in. and a height of 10 in.
    \nJack’s rhombus has base and height measures that are double those of Soshi’s rhombus.
    \narea = pq\/2.
    \narea = 12 x 10\/2.
    \narea = 120\/2.
    \narea = 60.
    \nso the area of Jack’s rhombus to the area of Soshi’s rhombus = 120.<\/p>\n

    Question 20.
    \nHigher Order Thinking<\/strong> The infield of a baseball diamond is in the shape of a rhombus. An infield cover with dimensions of 85 feet by 100 feet is used to protect the field during rainy weather. Will the cover protect the entire infield? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the rhombus = 90 ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe infield of a baseball diamond is in the shape of a rhombus.
    \nAn infield cover with dimensions of 85 feet by 100 feet is used to protect the field during rainy weather.
    \narea of the rhombus = pq\/2.
    \narea = 90 x 90\/2.
    \narea = 180\/2.
    \narea = 90.
    \nso the area of the rhombus = 90 ft.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 21.
    \nThe parking space shown at the right has an area of 209 ft2<\/sup>. A custom truck has rectangular dimensions of 13.5 ft by 8.5 ft. Can the truck fit in the parking space? Justify your answer.
    \n\"Envision<\/p>\n

    Answer:
    \nYes, the truck fits in the parking space.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe parking space shown at the right has an area of 209 ft2.
    \nA custom truck has rectangular dimensions of 13.5 ft by 8.5 ft.
    \narea of the parallelogram = b x h.
    \n209 = b x 19.
    \nb = 209\/19.
    \nb = 11.
    \n<\/sup>the rectangular dimensions of 13.5 ft by 8.5 ft.
    \narea = 13.5 x 8.5 ft.
    \narea = 114.75.<\/p>\n

    Lesson 7.2 Solve Triangle Area Problems<\/strong><\/h3>\n

    Solve & Discuss It!<\/strong>
    \nConnect point A to B, B to C, C to D, and D to A. Then draw a diagonal line connecting opposite vertices in the figure and find the area of each triangle formed.
    \nI can… find the areas of triangles.
    \n\"Envision<\/p>\n

    Use Structure
    \nWhat relationships do you see between the area of the parallelogram and the areas of the triangles?<\/p>\n

    Focus on math practices
    \nGeneralize What is a rule for finding the area of any triangle?<\/p>\n

    Answer:
    \nThe area of the triangle = b x h\/2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the triangle = b x h\/2.
    \nwhere b = base.
    \nh = height.
    \nso the area of the triangle = b x h\/2.<\/p>\n

    Essential Question<\/strong>
    \nHow can you find the area of a triangle?<\/p>\n

    Try It!<\/strong><\/p>\n

    Use the formula A = \\(\\frac{1}{2}\\)bh to find the area of the triangle.
    \n\"Envision
    \nThe area of the triangle is _________ cm2<\/sup><\/p>\n

    Answer:
    \nThe area of the triangle = 30 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea = 1\/2 x b x h.
    \narea = 1\/2 x 12 x 5.
    \narea = 1\/2 x 60.
    \narea = 30.
    \nso the area of the triangle = 30 sq cm.<\/p>\n

    Convince Me! Two identical triangles form a parallelogram with a base of 8 inches and a height of 6 inches. What is the area of each triangle? Explain.<\/p>\n

    Try It!<\/strong><\/p>\n

    Find the area of each triangle.
    \na.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 27 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 9cm x 6cm.
    \narea = 1\/2 x 54.
    \narea = 27 sq cm.<\/p>\n

    b.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 18 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 12m x 3m.
    \narea = 1\/2 x 36.
    \narea = 18 sq m.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use the formula A = \\(\\frac{1}{2}\\)bh to find the area of any triangle.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you find the area of a triangle?<\/p>\n

    Answer:
    \nThe area of the triangle = 1\/2bh.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nto find the area of any triangle, we can use the formula.
    \narea = 1\/2 bh.
    \nso the area of the triangle = 1\/2bh.<\/p>\n

    Question 2.
    \nReasoning<\/strong> If you cut a rectangle into 2 identical triangles, what type of triangles will they be?<\/p>\n

    Answer:
    \nThe triangles formed are right-angled triangles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of any triangle, we can use the formula.
    \narea = 1\/2 bh.
    \nso the area of the triangle = 1\/2bh.
    \nthe triangles formed are right-angled triangles.<\/p>\n

    Question 3.
    \nConstruct Arguments In Example 1, if the other diagonal were used to divide the parallelogram into two triangles, would the area of each of these triangles be half the area of the parallelogram? Explain.<\/p>\n

    Answer:
    \nYes, the area of each of these triangles is half the area of the parallelogram.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the parallelogram = b x h.
    \nwhere b = base.
    \nh = height.
    \nso the area of each of these triangles is half the area of the parallelogram.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 4-6, find the area of each triangle.
    \nQuestion 4.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 4 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 2ft x 4ft.
    \narea = 1\/2 x 8.
    \narea = 4 sq ft.<\/p>\n

    Question 5.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 7.35 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 4.2 x 3.5.
    \narea = 1\/2 x 14.7.
    \narea = 7.35 sq in.<\/p>\n

    Question 6.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 16.25 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 5 cm x 6.5 cm.
    \narea = 1\/2 x 32.5.
    \narea = 16.25 sq cm.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7-12, find the area of each triangle.
    \nQuestion 7.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 12 sq yd.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 6 yd x 4 yd.
    \narea = 1\/2 x 24 sq yd.
    \narea = 12 sq yd.<\/p>\n

    Question 8.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 15 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 6m x 5m.
    \narea = 1\/2 x 30.
    \narea = 15 sq m.<\/p>\n

    Question 9.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 91 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 14 cm x 13 cm.
    \narea = 1\/2 x 182.
    \narea = 91 sq cm.<\/p>\n

    Question 10.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 90 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 15 in x 12 in.
    \narea = 1\/2 x 180.
    \narea = 90 sq in.<\/p>\n

    Question 11.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 54 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 12 cm x 9 cm.
    \narea = 1\/2 x 108.
    \narea = 54 sq cm.<\/p>\n

    Question 12.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 24 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 8m x 6m.
    \narea = 1\/2 x 48.
    \narea = 24 sq m.<\/p>\n

    Question 13.
    \nThe vertices of a triangle are A(0, 0), B(3, 8), and C(9, 0). What is the area of this triangle?<\/p>\n

    Answer:
    \nThe area of this triangle = -4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe vertices of a triangle are A(0,0), B(3, 8), and C(9, 0).
    \nx1 = 0, x2 = 3, x3 = 9.
    \ny1 = 0, y2 = 8, y3 = 0.
    \narea = 1\/2[x1(y2-y3) + x2(y3 – y1) + x3(y1 – y2)].
    \narea = 1\/2[0(8) + 3(0) + 9(-8)].
    \narae = 1\/2(-8).
    \narea = -4.<\/p>\n

    Question 14.
    \nBe Precise The base of a triangle is 2 ft. The height of the triangle is 15 in. What is the area of the triangle in square inches?<\/p>\n

    Answer:
    \nArea of the triangle = 144 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe base of a triangle is 2 ft.
    \nThe height of the triangle is 15 in.
    \n1 ft = 12 in.
    \n2 ft = 24 in.
    \narea = b x h.
    \narea = 1\/2 x 24 x 12.
    \narea = 1\/2(288).
    \narea = 144 sq in.<\/p>\n

    \"Solve<\/p>\n

    Question 15.
    \nReasoning<\/strong> Ms. Lopez drew \u25b3 ABC, with a height of 6 inches and a base of 6 inches, and \u25b3RST, with a height of 4 inches and a base of 8 inches. Which triangle has the greater area? Use an area formula to justify your answer.<\/p>\n

    Answer:
    \nTriangle ABC has the greater area.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMs. Lopez drew \u25b3 ABC, with a height of 6 inches and a base of 6 inches, and \u25b3RST, with a height of 4 inches and a base of 8 inches.
    \narea of the trianglee ABC = 1\/2 x 6\u00a0 x 6.
    \nwhere b = base and h = height.
    \narea = 1\/2 x 36.
    \narea = 18 sq in.
    \narea of the triangle RST = 1\/2 x 8 x 4.
    \narea = 1\/2 x 32.
    \narea = 16 sq in.
    \nso the triangle ABC has the greater area.<\/p>\n

    Question 16.
    \nThe dimensions of the sail for Erica’s sailboat are shown. Find the area of the sail.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the sail = 67.5 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the sail = 1\/2 x b x h.
    \narea = 1\/2 x 9 x 15.
    \narea = 1\/2 x 135.
    \narea = 67.5 sq ft.
    \nso the area of the sail = 67.5 sq ft.<\/p>\n

    In 17 and 18, use the picture at the right.
    \n\"Envision
    \nQuestion 17.
    \nBe Precise What is the area in square millimeters of the yellow triangle outlined on the origami figure at the right?<\/p>\n

    Answer:
    \nArea = 2.64.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nb = 3 cm.
    \nh = 1.76 cm.
    \narea = 1\/2 x b x h.
    \narea = 1\/2 x 3 x 1.76.
    \narea = 5.28\/2.
    \narea = 2.64.<\/p>\n

    Question 18.
    \nThe nose of the origami dog is a right triangle with sides that are 2 cm, 3 cm, and 3.6 cm long. What is the area of this triangle?<\/p>\n

    Answer:
    \nArea = 3 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nb = 3 cm.
    \nh = 2 cm.
    \narea = 1\/2 x b x h.
    \narea = 1\/2 x 3 x 2.
    \narea = 6\/2.
    \narea = 3 sq cm.<\/p>\n

    Question 19.
    \nMichael is planting a garden in the shape of a right triangle. He wants 4 tickseed plants for each square meter of area. How many 25 m tickseed plants does Michael want in the garden?
    \n\"Envision<\/p>\n

    Answer:
    \nThe 25 m tickseed plants does Michae want in the garden = 84.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMichael is planting a garden in the shape of a right triangle.
    \nHe wants 4 tickseed plants for each square meter of area.
    \narea = 1\/2 x b x h.
    \nwhere b = base.
    \nh = height.
    \narea = 1\/2 x 7 x 24.
    \narea = 168\/2.
    \narea = 84.
    \nso the 25 m tickseed plants does Michae want in the garden = 84.<\/p>\n

    Question 20.
    \nHigher Order Thinking<\/strong> If you know the area and the height of a triangle, how can you find the base?
    \nAnswer:<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 21.
    \nSelect all expressions that represent the area of the given triangle.
    \n\"Envision<\/p>\n

    Answer:
    \nOptions A and E are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea = 1\/2 x 16 x 12.
    \nwhere b = 16 cm.
    \nheight = 12 cm.
    \narea = 1\/2 x 192.
    \narea = 96.
    \nso options A and E are correct.<\/p>\n

    Lesson 7.3 Find Areas of Trapezoids and Kites<\/h3>\n

    Explain It!<\/strong>
    \nThe European basketball key was changed from a trapezoid shape to a rectangle in 2010. The diagram shows the shape of the key before 2010 outlined in blue.<\/p>\n

    I can… find areas of trapezoids and kites.
    \n\"Envision<\/p>\n

    A. Construct Arguments Tim finds the area of the key by multiplying the base by the height. Does his strategy make sense?<\/p>\n

    Answer:
    \nYes.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \nwhere b = base.
    \nh = height.
    \narea = 1\/2 x 6 x 5.8.
    \narea = 1\/2 x 34.8.
    \narea = 17.4.<\/p>\n

    B. Use Structure How could Tim find the area of the trapezoid by decomposing it into shapes he knows? What is the area of the key?
    \nAnswer:<\/p>\n

    Focus on math practices
    \nUse Structure How can you find the area of this kite? Explain.
    \n\"Envision<\/p>\n

    Essential Question<\/strong>
    \nHow can you find the areas of trapezoids and kites?<\/p>\n

    Try It!<\/strong><\/p>\n

    How would you decompose this trapezoid to find its area? Find the area of the trapezoid.
    \n\"Envision
    \nAnswer:
    \nThe area of the trapezoid = 22.5 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the trapezoid = 11.25 + 5 + 6.25.
    \narea = 22.5.
    \nso the area of the trapezoid = 22.5 sq ft.<\/p>\n

    Convince Me! How is finding the area of the trapezoid in Example 1 different from finding the area of the trapezoid in the Try It!?<\/p>\n

    Try It!<\/strong><\/p>\n

    Find the area of the trapezoid and the area of the kite.
    \na.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the trapezoid = 144 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea = 24 cm + 24 cm + 96.
    \narea = 48 cm + 96.
    \narea = 144 sq cm.<\/p>\n

    b.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the kite = 72 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \neach triangle = 1\/2 x 24 x 3.
    \ntriangle = 1\/2 x 72.
    \ntriangle = 36 sq in.
    \nKite = 36 + 36.
    \nkite = 72 sq in.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can find the area of a trapezoid or a kite by decomposing the shapes into rectangles and triangles.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you find the areas of trapezoids and kites?<\/p>\n

    Answer:
    \nArea of the trapezoid = area of the triangle + area of the rectangle.
    \narea of the kite = area of the triangle.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the trapezoid = area of the triangle + area of the rectangle.
    \narea of the kite = area of the triangle.<\/p>\n

    Question 2.
    \nDraw a line to divide the pasture in Example 1 into two triangles. What are the measures of the bases and the heights of the two triangles?
    \nAnswer:<\/p>\n

    Question 3.
    \nConstruct Arguments In Example 3, how could you use 4 triangles to find the kite’s area?
    \nAnswer:<\/p>\n

    Do You Know How?<\/strong>
    \nIn 4-6, find the area of each trapezoid or kite.
    \nQuestion 4.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the kite = 16 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \nwhere b = 2m and height = 8 m.
    \narea = 1\/2 x 2 x 8.
    \narea = 16\/2.
    \narea = 8 sq m.
    \narea of the kite = 8 + 8.
    \narea = 16 sq m.<\/p>\n

    Question 5.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the kite = 6 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \nwhere b = 2cm and height = 3 cm.
    \narea = 1\/2 x 2 x 3.
    \narea = 6\/2.
    \narea = 3 sq cm.
    \narea of the kite = 3 + 3.
    \narea = 6 sq cm.<\/p>\n

    Question 6.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the kite = 90 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the triangle = 1\/2 x b x h.
    \nwhere b = 15 and height = 6 ft.
    \narea = 1\/2 x 15 x 6.
    \narea = 90\/2.
    \narea = 45 sq ft.
    \narea of the kite = 45 + 45.
    \narea = 90 sq ft.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7-12, find the area of each trapezoid or kite.
    \nQuestion 7.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the trapezoid = 168 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the trapezoid = area of each triangle + area of the rectangle.
    \narea of the triangle = 1\/2 x h x b.
    \narea = 1\/2 x 12 x 8.
    \narea = 1\/2 x 96.
    \narea = 48.
    \narea of the rectangle = l x w.
    \narea = 9 x 8.
    \narea = 72.
    \narea of the trapezoid = 48 + 48 + 72.
    \narea = 168 sq cm.<\/p>\n

    Question 8.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the trapezoid = 54 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the trapezoid = area of each triangle + area of the rectangle.
    \narea of the triangle = 1\/2 x h x b.
    \narea = 1\/2 x 6 x 4.
    \narea = 1\/2 x 24.
    \narea = 12.
    \narea of the rectangle = l x w.
    \narea = 5 x 6.
    \narea = 30.
    \narea of the trapezoid = 12 + 12 + 30.
    \narea = 24 + 30 sq cm.
    \narea = 54 sq cm.<\/p>\n

    Question 9.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the kite = 33 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the kite = area of the triangle + area of the triangle.
    \narea of the triangle = 1\/2 x b x h.
    \nwhere b = base and h = height.
    \narea = 1\/2 x 11 x 3.
    \narea = 1\/2 x 33.
    \narea = 16.5.
    \narea of the kite = 16.5 + 16.5.
    \narea = 33.<\/p>\n

    Question 10.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the kite = 112 sq yd.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the kite = area of the triangle + area of the triangle.
    \narea of the triangle = 1\/2 x b x h.
    \nwhere b = base and h = height.
    \narea = 1\/2 x 14 x 8.
    \narea = 1\/2 x 112.
    \narea = 56.
    \narea of the kite = 56 + 56.
    \narea = 112 sq yd.<\/p>\n

    Question 11.
    \nA sidewall of a building is shown below. What is the area of the wall?
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the trapezoid = 1020 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the trapezoid = area of the triangle + area of the rectangle.
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 6 x 30.
    \narea = 180\/2.
    \narea = 90.
    \narea of the rectangle = l x w.
    \narea = 28 x 30.
    \narea = 840.
    \narea of the trapezoid = 90 + 90 + 840.
    \narea = 180 + 840.
    \narea = 1020.<\/p>\n

    Question 12.
    \nBe Precise The window has the shape of a kite. How many square meters of glass were used to make the window?
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the Kite = 1225 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the kite = area of the triangle.
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 70 x 35.
    \narea = 2450\/2.
    \narea = 1225.
    \narea of the kite = 1225 + 1225.
    \narea = 1225 sq cm.<\/p>\n

    Question 13.
    \nThe area of the kite is 30 m2<\/sup>. What is the value of x? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe value of x = 6 m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of the kite = 30 sq m.
    \narea of the triangle = 1\/2 x b x h.
    \n30 = 1\/2 x 10 x h.
    \n30 = 5h.
    \nh = 30\/5.
    \nh = 6.<\/p>\n

    Question 14.
    \nMake Sense and Persevere Hunter drew two identical trapezoids and composed them to form a parallelogram. Use the area of the parallelogram to find the area of one trapezoid. Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the trapezoid = 36 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the parallelogram = b x h.
    \narea = 9 x 4.
    \narea = 36 sq ft.<\/p>\n

    Question 15.
    \nHigher Order Thinking<\/strong> A craftsman wants to build this symmetrical fiddle. He needs to know the area of the face of the fiddle. How could he use the measurements shown to find the area? Use your strategy to find the area of the face of the fiddle.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the fiddle = 35208 sq mm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the fiddle = 1\/2 x 326 x 216.
    \narea = 1\/2 x 70416.
    \narea = 35208.
    \nso the area of the fiddle = 35208 sq mm.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 16.
    \nMarique is making a large table in the shape of a trapezoid. She needs to calculate the area of the table. The longest side of the table is twice as long as the table’s width. Find the area of the table by decomposing the trapezoid into familiar shapes. Show your work.
    \n\"Envision<\/p>\n

    Answer:
    \nThe area of the trapezoid = 0.9375.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the trapezoid = area of the triangle + area of the rectangle.
    \narea of the triangle = 1\/2 x b x h.
    \narea = 1\/2 x 0.5 x 1.25.
    \narea = 1\/2 x 0.625.
    \narea = 0.3125.
    \narea of the rectangle = l x w.
    \narea = 0.5 x 1.25.
    \narea = 0.625.
    \narea = 0.3125 + 0.625.
    \narea = 0.9375.
    \nso the area of the trapezoid = 0.9375.<\/p>\n

    Lesson 7.4 Find Areas of Polygons<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nGabrielle wants to cover the floors of a room and a hallway in her dollhouse. She measured the room and hallway and sketched the floor plan below. How much felt does Gabrielle need?
    \nI can… find the areas of polygons.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 205 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the triangle + area of the triangle + area of the rectangle.
    \narea = 1\/2 x 15 x 10.
    \narea = 1\/2 x 150.
    \narea = 75.
    \narea = 1\/2 x 22 x 5.
    \narea = 1\/2 x 110.
    \narea = 55.
    \narea of the polygon = 75 + 55 + 75.
    \narea = 150 + 55.
    \narea = 205.<\/p>\n

    Make Sense and Persevere
    \nHow can you decompose the sketch into regular shapes?<\/p>\n

    Focus on math practices
    \nMake Sense and Persevere Show another way to find the area of the sketch.
    \n\"Envision<\/p>\n

    Essential Question<\/strong>
    \nHow can you find the areas of polygons?<\/p>\n

    Try It!<\/strong><\/p>\n

    Shari found the area of the patio by composing the shapes as shown at the right. How is Shari’s strategy different?
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 30 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the triangle + area of the triangle + area of the rectangle.
    \narea = 1\/2 x 3 x 2.
    \narea = 1\/2 x 6.
    \narea = 3.
    \narea = 1\/2 x 2 x 3.
    \narea = 1\/2 x 6.
    \narea = 3.
    \narea of the polygon = 3 + 3 + 24.
    \narea = 6 + 24.
    \narea = 30.<\/p>\n

    Convince Me! How could you decompose the figure in the Try It! into two rectangles?<\/p>\n

    Try It!<\/strong><\/p>\n

    Find the area of the shaded region in square units.
    \n\"Envision
    \nAnswer:<\/p>\n

    KEY CONCEPT<\/strong>
    \nThere are many ways to find the area of a polygon. You can decompose or compose shapes, or you can use addition or subtraction, to calculate the area.
    \nUse Addition
    \n\"Envision
    \nBlue triangle: A = \\(\\frac{1}{2}\\)(12)(6) = 36
    \nGreen triangle: A = \\(\\frac{1}{2}\\)(8)(6) = 24
    \nRectangle: A = (12)(6) = 72
    \n36 + 24 + 72 = 132
    \nThe area of the polygon is 132 cm2<\/sup>.<\/p>\n

    Use Subtraction
    \n\"Envision
    \nDraw a rectangle around the polygon.
    \nRectangle: A = 8 \u00d7 5 = 40
    \nTriangle: A = \\(\\frac{1}{2}\\) \u00d7 8 \u00d7 2 = 8
    \n40 – 8 = 32
    \nThe area of the polygon is 32 square units.<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you find the areas of polygons?<\/p>\n

    Answer:
    \nThe area of the polygon = area of the triangle + area of the triangle + area of the rectangle.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the triangle + area of the triangle + area of the rectangle.
    \narea of the triangle = 1\/2 x b x h.
    \nwhere b = base.
    \nh = height.
    \narea of the rectangle = l x w.
    \nwhere l = length.
    \nw = width.
    \nso the area of the polygon = area of the triangle + area of the triangle + area of the rectangle.<\/p>\n

    Question 2.
    \nDescribe a way in which you can use subtraction to find the area of the shape in Exercise 4.
    \nAnswer:<\/p>\n

    Question 3.
    \nModel with Math Describe how to break the floor plan in Example 3 into a trapezoid and a rectangle. Use coordinates to describe the line you can draw.
    \nAnswer:<\/p>\n

    Do You Know How?<\/strong>
    \nIn 4 and 5, find the area of each polygon.
    \nQuestion 4.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 280 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the small rectangle + area of the rectangle.
    \narea of small rectangle = 8 x 10.
    \narea = 80 sq in.
    \narea of the rectangle = 20 x 10.
    \narea = 200.
    \narea of the polygon = 80 + 200.
    \narea = 280 sq in.<\/p>\n

    Question 5.
    \nA polygon with vertices at (6, 2), (9,5), (12, 2), (12, -4), and (6, -4)
    \n\"Envision
    \nAnswer:<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 6-9, find the area of each polygon or shaded region.
    \nQuestion 6.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 200 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the small rectangle + area of the small rectangle + area of the big rectangle.
    \narea of the small rectangle = 15 x 3.
    \narea = 45.
    \narea of the another small rectangle = 15 x 4.
    \narea = 60.
    \narea of the big rectangle = 19 x 5.
    \narea = 95.
    \narea of the polygon = 45 + 60 + 95.
    \narea of the polygon = 200.<\/p>\n

    Question 7.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 232 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the small rectangle + area of the small rectangle + area of the big rectangle.
    \narea of the small rectangle = 10 x 2.
    \narea = 20.
    \narea of the another small rectangle = 10 x 2.
    \narea = 20.
    \narea of the big rectangle = 16 x 12.
    \narea = 192.
    \narea of the polygon = 20 + 20 + 192.
    \narea of the polygon = 232.<\/p>\n

    Question 8.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 24 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the small rectangle + area of the small rectangle + area of the big rectangle.
    \narea of the small rectangle = 2 x 2.
    \narea = 4.
    \narea of the another small rectangle = 2 x 2.
    \narea = 4.
    \narea of the big rectangle = 4 x 4.
    \narea = 16.
    \narea of the polygon = 16 + 4 + 4.
    \narea of the polygon = 24.<\/p>\n

    Question 9.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 76 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the small triangle + area of the small triangle + area of the big rectangle.
    \narea of the small triangle = 1\/2(4 x 3).
    \narea = 6 .
    \narea of the another small rectangle = 1\/2(3 x 4).
    \narea = 6.
    \narea of the big rectangle = 8 x 8.
    \narea = 64.
    \narea of the polygon = 64 + 6 + 6.
    \narea of the polygon = 76.<\/p>\n

    In 10 and 11, find the area in square units of each polygon.
    \nQuestion 10.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 15 sq units.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the small triangle + area of the small triangle + area of the big triangle.
    \narea of the small triangle = 1 x 3.
    \narea = 3.
    \narea of the another small triangle = 1 x 3.
    \narea = 3.
    \narea of the big rectangle = 3 x 3.
    \narea = 9.
    \narea of the polygon = 3 + 3 + 9.
    \narea of the polygon = 15.<\/p>\n

    Question 11.
    \n\"Envision<\/p>\n

    Answer:
    \nArea of the polygon = 15 sq units.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the polygon = area of the small triangle + area of the small triangle + area of the big triangle.
    \narea of the small triangle = 1 x 3.
    \narea = 3.
    \narea of the another small triangle = 1 x 3.
    \narea = 3.
    \narea of the big rectangle = 3 x 3.
    \narea = 9.
    \narea of the polygon = 3 + 3 + 9.
    \narea of the polygon = 15.<\/p>\n

    Question 12.
    \nBe Precise Diego is designing an exercise room. How many square feet of rubber flooring will he need to cover the floor? The product is sold in whole square yards. How many square yards should Diego buy? Explain.
    \n\"Envision
    \nAnswer:<\/p>\n

    In 13 and 14, use the diagram at the right.
    \n\"Envision
    \nQuestion 13.
    \nDavid drew this diagram of a picture frame that he is going to make. Each square represents 1 square inch. What is the area of the picture frame?
    \nAnswer:<\/p>\n

    Question 14.
    \nUse Structure How could you find the area of the picture frame without decomposing the frame into smaller shapes?
    \nAnswer:<\/p>\n

    Question 15.
    \nHigher Order Thinking<\/strong> Isabella has three rectangular cards that are 4 inches by 5 inches. How can she arrange the cards, without overlapping, to make one larger polygon with the smallest possible perimeter? How will the area of the polygon compare to the combined area of the three cards?
    \n\"Envision
    \nAnswer:<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 16.
    \nSelect all expressions that can be used to find the area of the given polygon.
    \n\"Envision
    \n\u2610 (2 \u00d7 5) + (6 \u00d7 4)
    \n\u2610 (5 \u00d7 2) + 2 \u2022 \\(\\frac{1}{2}\\)(3 \u00d7 4)
    \n\u2610 (6 \u00d7 5) \u2013 (3 \u00d7 4)
    \n\u2610 ( 6\u00d7 9) \u2013 (3 \u00d7 4)
    \n\u2610 (5 \u00d7 2) + \\(\\frac{1}{2}\\)(2 + 2 + 2) \u00d7 4]<\/p>\n

    Answer:
    \nOptions A and E are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n(2 x 5) + (6 x 4).
    \n10 + 24.
    \n34.
    \nso options A and E are correct.<\/p>\n

    Question 17.
    \nWhat is the area of the polygon at the right?
    \n\"Envision
    \nA. 86 square units
    \nB. 78 square units
    \nC. 70 square units
    \nD. 68 square units<\/p>\n

    Answer:
    \nOption C is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n-5 x 8 = -40.
    \n-5 x 6 = -30.
    \n-40 + (-30).
    \n70 square units.<\/p>\n

    Topic 7 Mid-Topic Checkpoint<\/h3>\n

    Question 1.
    \nVocabulary<\/strong> How many pairs of opposite sides are parallel in a trapezoid? How is this different from a parallelogram? Lesson 7-3
    \nAnswer:<\/p>\n

    Question 2.
    \nCalculate the area of each figure at the right. Which figure has the greatest area? Lessons 7-1, 7-2, and 7-3
    \n\"Envision
    \nA. triangle
    \nB. parallelogram
    \nC. trapezoid<\/p>\n

    Answer:
    \nOption C is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe polygon are triangle, parallelogram, and trapezoid.
    \narea of the triangle = l x b.
    \narea = 6 x 8.
    \narea = 48.
    \narea of the parallelogram = 8.5 x 4.
    \narea = 34.
    \narea of trapezoid = 3 x 4 + 9 x 6.
    \narea = 12 + 54.
    \narea = 66.
    \nso option C is correct.<\/p>\n

    Question 3.
    \nAn earring has the shape of a rhombus. The height is 5.2 mm and the area of the earring is 39 mm2. What is the length of each side of the earring? Lesson 7-1<\/p>\n

    Answer:
    \nThe length of each side of the earring = 7.5 mm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn earring has the shape of a rhombus.
    \nThe height is 5.2 mm and the area of the earring is 39 mm2.
    \narea = l x h.
    \n39 = l x 5.2.
    \nl = 39\/5.2.
    \nl = 7.5.
    \nso the length of each side of the earring = 7.5 mm.<\/p>\n

    Question 4.
    \nShane wrapped the kite at the right with paper. How many square inches of paper did Shane use to cover the front and back? Lesson 7-3
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 288 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nShane wrapped the kite at the right with paper.
    \narea of the rhombus = area of each triangle + area of kite.
    \narea of triangle = 1\/2(32)(9).
    \narea of triangle = 288\/2.
    \narea = 144.
    \narea of kite = 144 + 144.
    \narea = 288.<\/p>\n

    Question 5.
    \nExplain one way to find the area of the polygon at the right. Then find the area in square units. Lesson 7-4
    \n\"Envision
    \nAnswer:<\/p>\n

    Topic 7 Mid-Topic Performance Task<\/h3>\n

    Kira hires a contractor to build a new deck in her backyard. A design for the deck is shown.
    \n\"Envision<\/p>\n

    PART A
    \nKira found the area of the deck by decomposing it into two identical trapezoids. Describe another strategy you could use to find the area of the deck.<\/p>\n

    Answer:
    \nThe area of the deck = 204 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of trapezoid = area of the triangle + area of the rectangle.
    \narea of triangle = 1\/2(12)
    \narea = 6.
    \narea of rectangle = 16 x 12.
    \narea = 192.
    \narea of trapezoid = 6 + 6 + 192.
    \narea = 12 + 192.
    \narea = 204.<\/p>\n

    PART B
    \nWhich expression can you use to find the area of the deck? Select all that apply.
    \n\u2610 (16 \u00d7 12) + 2(\\(\\frac{1}{2}\\) \u00d7 12 \u00d7 5)
    \n\u2610 (26 \u00d7 12) + 2(\\(\\frac{1}{2}\\) \u00d7 12 \u00d7 5)
    \n\u2610 (26 \u00d7 12) \u2013 4(\\(\\frac{1}{2}\\) \u00d7 6 \u00d7 5)
    \n\u2610 (16 \u00d7 6) + 2(\\(\\frac{1}{2}\\) \u00d7 6 \u00d7 5) + (16 \u00d7 6) + 2(\\(\\frac{1}{2}\\) \u00d7 6 \u00d7 5)
    \n\u2610 (16 \u00d7 12) + 2(\\(\\frac{1}{2}\\) \u00d7 12 \u00d7 10)<\/p>\n

    Answer:
    \nOption A is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \narea of the deck = area of the triangle + area of the rectangle.
    \narea = 1\/2 x 12.
    \narea = 6.
    \narea of rectangle = 16 x 12.
    \narea = 192.
    \narea of trapezoid = 6 + 6 + 192.
    \narea = 12 + 192.
    \narea = 204.<\/p>\n

    PART C
    \nA second design for Kira’s deck is shown at the right. Find the areas of the two deck designs. Which design will give Kira the deck with the greater area? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 216 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA second design for Kira’s deck is shown at the right.
    \narea of the polygon = area of the triangle + area of the rectangle.
    \narea of triangle = 1\/2(8)(6).
    \narea = 1\/2(48).
    \narea = 24.
    \narea of rectangle = 6 x 16.
    \narea = 96.
    \narea of up rectangle = 12 x 8.
    \narea = 96.
    \narea of polygon = 24 + 96 + 96.
    \narea = 216 sqft.<\/p>\n

    Lesson 7.5 Represent Solid Figures Using Nets<\/h3>\n

    Explore It!<\/strong>
    \nJamal is breaking down items for recycling and wonders what this box will look like when it is unfolded and flat.<\/p>\n

    I can… represent solid figures using nets.
    \n\"Envision<\/p>\n

    A. How do the sides of the box help you think about what the unfolded box will look like?
    \nAnswer:<\/p>\n

    B. How can you use the grid to represent the unfolded box?
    \n\"Envision
    \nAnswer:<\/p>\n

    Focus on math practices
    \nReasoning is there another way to represent the unfolded box on the grid? Explain.<\/p>\n

    Essential Question<\/strong>
    \nHow do you classify and represent solid figures?<\/p>\n

    Try It!<\/strong><\/p>\n

    Classify this solid figure.
    \n\"Envision<\/p>\n

    Answer:
    \nThe figure is Triangular pyramid.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is triangular pyramid.
    \nvolume of triangular pyramid = 1\/3 x B X H.
    \nvolume = 1\/3 x 1\/2 x BH.
    \nvolume = 1\/6 Bh.<\/p>\n

    Convince Me! What attributes of a solid figure should you identify to classify it as a polyhedron?<\/p>\n

    Try It!<\/strong><\/p>\n

    Identify the solid from its net.
    \n\"Envision
    \nShape of polygonal faces: ___________
    \nShape of base(s): ___________
    \nThis is a net of a ___________.<\/p>\n

    Answer:
    \nThe figure is a polyhedron.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nshape of polygonal faces = 3.
    \nshape od base = 3.
    \nthis is a net of polyhedron.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use nets to represent solid figures.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How do you classify and represent solid figures?<\/p>\n

    Answer:
    \nThe solid figures are prism and pyramids.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nprism has more than one base.
    \npyramid has only one base.
    \nprism does not have any face.
    \npyramid has its face.<\/p>\n

    Question 2.
    \nUse Structure Explain the difference between a vertex and an edge.<\/p>\n

    Answer:
    \nVertex is the highest point or apex.
    \nEdge is the outside area or a surface.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nvertex is the highest point or top or apex.
    \nedge is the outside area or a surface.<\/p>\n

    Question 3.
    \nBe Precise Explain the difference between a pyramid and a prism.<\/p>\n

    Answer:
    \nThe solid figures are prism and pyramids.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nprism has more than one base.
    \npyramid has only one base.
    \nprism does not have any face.
    \npyramid has its face.<\/p>\n

    Question 4.
    \nDescribe the net of a triangular prism.
    \nAnswer:<\/p>\n

    Do You Know How?<\/strong>
    \nIn 5 and 6, classify the solid figures.
    \nQuestion 5.
    \n\"Envision
    \nAnswer:
    \nThe figure is Triangular pyramid.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is triangular pymarid.
    \nvolume = 1\/6 Bh.
    \nwhere b = base.
    \nh = height.
    \nso the figure is triangular pyramid.<\/p>\n

    Question 6.
    \n\"Envision<\/p>\n

    Answer:
    \nThe figure is rectangular prism.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is a rectangular prism.
    \nvolume of prism = b x h.<\/p>\n

    In 7 and 8, identify each solid from its net.
    \nQuestion 7.
    \n\"Envision<\/p>\n

    Answer:
    \nThe figure is pyramid.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe net is pyramid.
    \npyramid has face, base, and vertex.
    \nso the figure is pyramid.<\/p>\n

    Question 8.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 9.
    \nDraw a net of a rectangular prism that has a height of 2 units and bases that are 3 units long and 1 unit wide.
    \n\"Envision
    \nAnswer:<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 10-12, classify the solid figures.
    \nQuestion 10.
    \n\"Envision<\/p>\n

    Answer:
    \nThe figure is rectangular prism.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is a rectangular prism.
    \nvolume of prism = l x w x h.
    \nwhere l = length.
    \nw = width.
    \nh = height.<\/p>\n

    Question 11.
    \n\"Envision<\/p>\n

    Answer:
    \nThe figure is Triangular pyramid.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is triangular pymarid.
    \nvolume = 1\/6 Bh.
    \nwhere b = base.
    \nh = height.
    \nso the figure is triangular pyramid.<\/p>\n

    Question 12.
    \n\"Envision<\/p>\n

    Answer:
    \nThe figure is a triangular pyramid.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is a triangular pyramid.
    \nvolume = 1\/3 x b x h.
    \nb = base area.
    \nh = height.<\/p>\n

    In 13-15, identify each solid from its net.
    \nQuestion 13.
    \n\"Envision<\/p>\n

    Answer:
    \nThe figure is pyramid.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe net is pyramid.
    \npyramid has face, base, and vertex.
    \nso the figure is pyramid.<\/p>\n

    Question 14.
    \n\"Envision<\/p>\n

    Answer:
    \nVolume of the prism = 1\/2bhl.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is triangular prism.
    \nvolume of the prism = 1\/2 x bhl.
    \nwhere b = base.
    \nh = height.
    \nl = length.<\/p>\n

    Question 15.
    \n\"Envision
    \nAnswer:
    \nThe figure is rectangular prism.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is a rectangular prism.
    \nvolume of prism = l x w x h.
    \nwhere l = length.
    \nw = width.
    \nh = height.<\/p>\n

    Question 16.
    \nRyan is going to draw a net of a rectangular prism. How many rectangles should there be in his drawing?<\/p>\n

    Answer:
    \nThe figure is rectangular prism.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe figure is a rectangular prism.
    \nvolume of prism = l x w x h.
    \nwhere l = length.
    \nw = width.
    \nh = height.<\/p>\n

    Question 17.
    \nKayla is going to draw a net of a square pyramid. How many triangles should there be in her drawing?<\/p>\n

    Answer:
    \nThe formula of square pyramid = a x a x h\/3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe formula of square pyramid.
    \nv = a x a x h\/3.
    \nwhere a = base edge.
    \nh = height.<\/p>\n

    Question 18.
    \nMake Sense and Persevere Zari folds the net below into a model of a solid figure. How many edges, faces, and vertices does the model have?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of faces, edges, and vertices = 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of edges = 3.
    \nthe number of faces = 3.
    \nthe number of vertices = 3.<\/p>\n

    Question 19.
    \nCritique Reasoning<\/strong> Tomas says that the net below can be folded to make a rectangular prism. Do you agree with Tomas? Explain.
    \n\"Envision
    \nAnswer:<\/p>\n

    In 20-22, use the table at the right.
    \n\"Envision
    \nQuestion 20.
    \nLook for Relationships The Swiss mathematician Leonhard Euler (OY-ler) and the French mathematician Ren\u00e9 Descartes (d\u00e3 KART) both discovered a pattern in the numbers of edges, vertices, and faces of polyhedrons. Complete the table. Describe a pattern in the table.
    \nAnswer:<\/p>\n

    Question 21.
    \nHigher Order Thinking<\/strong> Write an equation that relates the number of edges, E, to the number of faces, F, and vertices, V.
    \nAnswer:<\/p>\n

    Question 22.
    \nUse the equation that you wrote in Exercise 21 to find the number of vertices of a cube, which has 12 edges and 6 faces.
    \nAnswer:<\/p>\n

    Question 23.
    \nCorey bought the mailing tube shown at the right to mail a poster of the Gators Little League baseball team.
    \n\"Envision
    \na. The mailing tube has the shape of which polyhedron?
    \nAnswer:<\/p>\n

    b. How many faces does the mailing tube have?
    \nAnswer:<\/p>\n

    c. When Corey bought the mailing tube, it was unfolded and looked like a net. What polygons would Corey have seen in the unfolded mailing tube?
    \nAnswer:<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 24.
    \nDraw a net of a square pyramid for which the base is 2 units long and the height of each triangular face is 5 units.
    \n\"Envision
    \nAnswer:<\/p>\n

    3-ACT MATH<\/strong><\/p>\n

    3-Act Mathematical Modeling: That’s a Wrap
    \n\"Envision<\/p>\n

    ACT 1<\/strong>
    \nQuestion 1.
    \nAfter watching the video, what is the first question that comes to mind?
    \nAnswer:<\/p>\n

    Question 2.
    \nWrite the Main Question you will answer.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 3.
    \nConstruct Arguments Predict an answer to this Main Question Explain your prediction.
    \nAnswer:<\/p>\n

    Question 4.
    \nOn the number line below, write a number that is too small to be the answer. Write a number that is too large.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 5.
    \nPlot your prediction on the same number line.
    \nAnswer:<\/p>\n

    ACT 2<\/strong>
    \nQuestion 6.
    \nWhat information in this situation would be helpful to know? How would you use that information?
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 7.
    \nUse Appropriate Tools What tools can you use to solve the problem? Explain how you would use them strategically.
    \nAnswer:<\/p>\n

    Question 8.
    \nModel with Math Represent the situation using mathematics. Use your representation to answer the Main Question.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 9.
    \nWhat is your answer to the Main Question? Is it higher or lower than your prediction? Explain why.
    \nAnswer:<\/p>\n

    ACT 3<\/strong>
    \nQuestion 10.
    \nWrite the answer you saw in the video.
    \nAnswer:<\/p>\n

    Question 11.
    \nReasoning Does your answer match the answer in the video? If not, what are some reasons that would explain the difference?
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 12.
    \nMake Sense and Persevere Would you change your model now that you know the answer? Explain.
    \n\"Envision
    \nAnswer:<\/p>\n

    Reflect<\/strong>
    \nQuestion 13.
    \nModel with Math Explain how you used a mathematical model to represent the situation. How did the model help you answer the Main Question?
    \nAnswer:<\/p>\n

    Question 14.
    \nLook for Relationships Explain how the dimensions of the gift are related to the area of its net.
    \nAnswer:<\/p>\n

    SEQUEL<\/strong>
    \nQuestion 15.
    \nCritique Reasoning A classmate says that if all dimensions of the gift were doubled, you would need twice as many squares. Do you agree? Justify his reasoning or explain his error.
    \n\"Envision
    \nAnswer:<\/p>\n

    Lesson 7.6 Find Surface Areas of Prisms<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nMarianne orders boxes to pack gifts. When they arrive, she finds flat pieces of cardboard as shown below. Marianne needs to cover each face of the boxes with green paper. What is the least amount of paper needed to cover each box? Explain.
    \nI can… draw a net of a prism and use it to find the prism’s surface area
    \n\"Envision<\/p>\n

    Make Sense and Persevere
    \nWhat solid figure does this net represent?<\/p>\n

    Focus on math practices
    \nMake Sense and Persevere Suppose Marianne has only one large sheet of green paper that is 15 inches by 30 inches. Is the area of this sheet of paper great enough to cover all of the faces of one box? Explain.<\/p>\n

    Essential Question<\/strong>
    \nHow can you find the surface area of a prism?<\/p>\n

    Try It!<\/strong><\/p>\n

    Use the net and the formula to find the surface area of the prism.
    \nSA = 2(lw) + 2(wh) + 2(lh)
    \n\"Envision<\/p>\n

    Answer:
    \nSurface area = 52 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \nwhere l = length, w = width, and h = height.
    \nsurface area = 2(8) + 2(6) + 2(12).
    \nsurface area = 16 + 12 + 24.
    \nsurface area = 52 sq cm.<\/p>\n

    Convince Me! Why are tw, wh, and th each multiplied by 2 in the formula?
    \n\"Envision<\/p>\n

    Try It!<\/strong><\/p>\n

    Find the surface area of each prism.
    \na.
    \n\"Envision<\/p>\n

    Answer:
    \nSurface area = 52 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \nwhere l = length, w = width, and h = height.
    \nsurface area = 2(17.64) + 2(17.64) + 2(17.64).
    \nsurface area = 35.28 + 35.28 + 35.28.
    \nsurface area = 105.84 sq cm.<\/p>\n

    b.
    \n\"Envision<\/p>\n

    Answer:
    \nSurface area = 214 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \nwhere l = length, w = width, and h = height.
    \nsurface area = 2(42) + 2(35) + 2(30).
    \nsurface area = 84 + 70 + 60.
    \nsurface area = 214 sq ft.<\/p>\n

    KEY CONCEPT<\/strong>
    \nTo find the surface area of a prism, use a net or a formula.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you find the surface area of a prism?<\/p>\n

    Answer:
    \nArea = 216.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(10)(6) + 2(6)(3) + 2(10)(3).
    \narea = 2(60) + 2(18) + 2(30).
    \narea = 120 + 36 + 60.
    \narea = 216.<\/p>\n

    Question 2.
    \nConstruct Arguments<\/strong> Could you use the formula for the surface area of a rectangular prism to find the surface area of a cube? Explain.
    \nAnswer:<\/p>\n

    Question 3.
    \nLook for Relationships Which faces of a rectangular prism always have the same area?
    \nAnswer:<\/p>\n

    Question 4.
    \nGeneralize What does it mean to find surface area?
    \nAnswer:<\/p>\n

    Do You Know How?<\/strong>
    \nIn 5-7, find the surface area of each prism.
    \nQuestion 5.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 160 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(10)(5) + 2(5)(2) + 2(10)(2).
    \narea = 2(50) + 2(10) + 2(20).
    \narea = 100 + 20 + 40.
    \narea = 160.<\/p>\n

    Question 6.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 294.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(7)(7) + 2(7)(7) + 2(7)(7).
    \narea = 2(49) + 2(49) + 2(49).
    \narea = 98 + 98 + 98.
    \narea = 294.<\/p>\n

    Question 7.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 30.4 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(2)(2.8) + 2(2.8)(2) + 2(2)(2).
    \narea = 2(5.6) + 2(5.6) + 2(4).
    \narea = 11.2 + 11.2 + 8.
    \narea = 30.4.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 8-13, find the surface area of each prism.
    \nQuestion 8.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 384 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(8)(8) + 2(8)(8) + 2(8)(8).
    \narea = 2(64) + 2(64) + 2(64).
    \narea = 128 + 128 + 128.
    \narea = 384.<\/p>\n

    Question 9.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 114 sq yd.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(3)(5) + 2(5)(6) + 2(4)(3).
    \narea = 2(15) + 2(30) + 2(12).
    \narea = 30 + 60 + 24.
    \narea = 114.<\/p>\n

    Question 10.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 550 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(10)(5) + 2(5)(15) + 2(10)(15).
    \narea = 2(50) + 2(75) + 2(150).
    \narea = 100 + 150 + 300.
    \narea = 550 sq cm.<\/p>\n

    Question 11.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 73 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(7)(2) + 2(2.5)(2) + 2(7)(2.5).
    \narea = 2(14) + 2(5) + 2(17.5).
    \narea = 28 + 10 + 35.
    \narea = 73 sq m.<\/p>\n

    Question 12.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 358.4 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(8)(7.2) + 2(7.2)(8) + 2(8)(8).
    \narea = 2(57.6) + 2(57.6) + 2(64).
    \narea = 115.2 + 115.2 + 128.
    \narea = 358.4 sq cm.<\/p>\n

    Question 13.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 864 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(12)(12) + 2(12)(12) + 2(12)(12).
    \narea = 2(144) + 2(144) + 2(144).
    \narea = 288 + 288 + 288.
    \narea = 864 sq ft.<\/p>\n

    Question 14.
    \nCritique Reasoning Jacob says that the surface: area of the cube is less than 1,000 cm2<\/sup>. Do you agree with Jacob? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 216 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(10)(6) + 2(6)(3) + 2(10)(3).
    \narea = 2(60) + 2(18) + 2(30).
    \narea = 120 + 36 + 60.
    \narea = 216 sq cm.<\/p>\n

    Question 15.
    \nYou want to wrap a paperweight shaped like the triangular prism shown. How many square inches of wrapping paper do you need to completely cover the prism?
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 128 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(4)(4) + 2(8)(4) + 2(4)(4).
    \narea = 2(16) + 2(32) + 2(16).
    \narea = 32 + 64 + 32.
    \narea = 128 sq in.<\/p>\n

    Question 16.
    \nSasha has 2 blocks of clay shaped like the rectangular prism below. She joins them to form a rectangular prism with a length of 12 inches. What is the surface area of the larger prism?
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 56 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(6)(2) + 2(2)(2) + 2(6)(2).
    \narea = 2(12) + 2(4) + 2(12).
    \narea = 24 + 8 + 24.
    \narea = 56 sq in.<\/p>\n

    Question 17.
    \nA rectangular prism has a length of 12 cm, a height of 6 cm, and a width of 4 cm. Use the formula SA = 2(lw) + 2(wh) + 2(lh) to find the surface area of the rectangular prism.<\/p>\n

    Answer:
    \nArea = 288 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(12)(4) + 2(4)(6) + 2(12)(6).
    \narea = 2(48) + 2(24) + 2(72).
    \narea = 96 + 48 + 144.
    \narea = 288 sq cm.<\/p>\n

    In 18 and 19, use the diagram of the birdhouse.
    \n\"Envision<\/p>\n

    Answer:
    \nArea = 210 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the prism = 2(lw) + 2(wh) + 2(lh).
    \narea = 2(5)(5) + 2(5)(8) + 2(5)(8).
    \narea = 2(25) + 2(40) + 2(40).
    \narea = 50 + 80 + 80.
    \narea = 210.<\/p>\n

    Question 18.
    \nKali wants to build this birdhouse. She bought a 24-inch by 48-inch sheet of plywood. Does Kali have enough wood to make the birdhouse? Explain.<\/p>\n

    Answer:
    \nYes, kali has enough wood to make the birdhouse.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKali wants to build this birdhouse.
    \nShe bought a 24-inch by 48-inch sheet of plywood.
    \n24 x 48.
    \n1152 sq in.
    \nso kali has enough wood to make the birdhouse.<\/p>\n

    Question 19.
    \nReasoning kali decides to paint the birdhouse. She has a pint of paint that covers 32.5 ft2<\/sup> of surface. How can you tell that Kali has enough paint without calculating?<\/p>\n

    Answer:
    \nYes, kali has enough paint without calculating.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nkali decides to paint the birdhouse.
    \nShe has a pint of paint that covers 32.5 ft2<\/sup> of the surface.
    \n24 x 48.
    \n1152 sq in.
    \nso kali has enough paint without calculating.<\/p>\n

    Question 20.
    \nUse the formula SA = 2lw + 2lh + 2wh to find the surface area for a rectangular prism with a length, l, of 2.3 inches; a width, w, of 1.1 inches; and a height, h, of 3 inches.<\/p>\n

    Answer:
    \nArea = 25.92 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nlength = 2.3 in.
    \nwidth = 1.1 in.
    \nheight = 3 in.
    \nsurface area for a rectangular prism = 2lw + 2lh + 2wh.
    \narea = 2(2.3 x 1.2) + 2(2.3 x 3) + 2(1.1 x 3).
    \narea = 2(2.76) + 2(6.9) + 2(3.3).
    \narea = 5.52 + 13.8 + 6.6.
    \narea = 25.92 sq in.<\/p>\n

    Question 21.
    \nMake Sense and Persevere Justine wants to wrap a shipping box shaped like a rectangular prism. The box is 28 inches tall and has a square base with sides that each measure 2 inches. How much paper will Justine use?<\/p>\n

    Answer:
    \nJustin uses 232 sq in of paper.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJustine wants to wrap a shipping box shaped like a rectangular prism.
    \nThe box is 28 inches tall and has a square base with sides that each measure 2 inches.
    \narea = 2lw + 2wh + 2lh.
    \narea = 2(2 x 2) + 2(2 x 28) + 2(2 x 28).
    \narea = 2(4) + 2(56) + 2(56).
    \narea = 8 + 112 + 112.
    \narea = 232 sq in.
    \nso Justin uses 232 sq in of paper.<\/p>\n

    Question 22.
    \nHigher Order Thinking<\/strong> Margaret wants to cover a footrest in the shape of a rectangular prism with cotton fabric. The footrest is 18 inches by 12 inches by 10 inches. Margaret has 1 square yard of fabric. Can she completely cover the footrest? Explain.<\/p>\n

    Answer:
    \nYes, she completely covers the footrest.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMargaret wants to cover a footrest in the shape of a rectangular prism with cotton fabric.
    \nThe footrest is 18 inches by 12 inches by 10 inches.
    \nMargaret has 1 square yard of fabric.
    \narea = 2lw + 2wh + 2lh.
    \narea = 2(18 x 12) + 2(12 x 10) + 2(18 x 10).
    \narea = 2(216) + 2(120) + 2(180).
    \narea = 432 + 240 + 360.
    \narea = 1032 sq in.
    \n1 square yd = 1296 sq in.
    \nyes, she completely covers the footrest.<\/p>\n

    Question 23.
    \nA cube has a surface area of 486 in.2<\/sup>. Can the length of each side of the cube be 11 in.? Explain.<\/p>\n

    Answer:
    \nNo, the length of each side of the cube is 9 in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA cube has a surface area of 486 sq.
    \nthe surface area of the cube = 6 a x a.
    \narea = 6 x 9 x 9.
    \n486 = 81 x 6.
    \nno the length of each side of the cube is 9 in.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 24.
    \nUsing nets, find the surface area, in square feet, of a rectangular prism with a height of 2 feet, a length of 4.2 feet, and a width of 2.5 feet.<\/p>\n

    Answer:
    \nSurface area = 47.8 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nrectangular prism with a height of 2 feet, a length of 4.2 feet, and a width of 2.5 feet.
    \nsurface area = 2lw + 2wh + 2lh.
    \narea = 2(2 x 4.2) + 2(4.2 x 2.5) + 2(2 x 2.5).
    \narea = 2(8.4) + 2(10.5) + 2(5).
    \narea = 16.8 + 21 + 10.
    \narea = 47.8 sq ft.<\/p>\n

    Question 25.
    \nThe surface area of a cube is 273.375 square feet. The net of the prism is shown.
    \n\"Envision
    \nWhat are the possible dimensions of the cube in feet?
    \nA. 6, 6, 6
    \nB. 6, 6.75, 6.75
    \nC. 6.5, 6.5, 6.5
    \nD. 6.75, 6.75, 6.75<\/p>\n

    Answer:
    \nOption B is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the cube = 6a x a.
    \nsurface area = 6 x 6.75 x 6.75.
    \narea = 6 x 45.5625.
    \narea = 273.375 cubic feet.
    \nso option B is correct.<\/p>\n

    Lesson 7.7 Find Surface Areas of Pyramids<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nThe fence in Marci’s front yard has decorative tops, in the shape of square pyramids, every 6 feet. Marci paints each face of each top a different color before attaching the tops to the fence. What is the total surface area that she paints on each decorative top?
    \nI can… draw a net of a pyramid and use it to find the pyramid’s surface area.
    \n\"Envision<\/p>\n

    Use Appropriate Tools
    \nWhat tools can you use to help solve this problem?<\/p>\n

    Focus on math practices
    \nUse Structure Suppose the side lengths of the square base of each decorative top are increased by 2 inches. What is the total surface area of each top?<\/p>\n

    Essential Question<\/strong>
    \nHow can you find the surface area of a pyramid?<\/p>\n

    Answer:
    \nThe surface area of the pyramid = A + 1\/2 ps.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the pyramid = A + 1\/2 ps.
    \nwhere A = area of the base.
    \np = perimeter of the base.
    \ns = slant height.<\/p>\n

    Try It!<\/strong><\/p>\n

    Find the surface area of the square pyramid. Draw a net to find the areas of the base and each face of the pyramid.
    \n\"Envision<\/p>\n

    Answer:
    \nThe surface area of the square pyramid = 528 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nbase edge = 6 cm.
    \nheight = 8 cm.
    \nsurface area of the square pyramid = axa + 2a square root of axa\/4 + h x h.
    \narea = 36 + 12 square root 36\/4 + 64.
    \narea = 48 6\/2+\u00a0 \u00a08.
    \narea = 48 x 3 + 8.
    \narea = 48 x 11.
    \narea = 528 sq cm.<\/p>\n

    Convince Me! For the pyramid in the Try It!, what values would you use for B, n, and A in the formula SA = B + (nA)?<\/p>\n

    Try It!<\/strong><\/p>\n

    Draw a net and find the surface area of the triangular pyramid. Find the area (T) of each equilateral triangle.
    \n\"Envision
    \nT = \\(\\frac{1}{2}\\)bh
    \nT = \\(\\frac{1}{2}\\) _______ _______
    \n= ________
    \nThe area of each equilateral triangle is __________ m2<\/sup>.<\/p>\n

    Answer:
    \nThe area of each equilateral triangle is 7 sq m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe area of each equilateral triangle is 1\/2 x bh.
    \narea = 1\/2 x 4 x 3.5.
    \narea = 2 x 3.5.
    \narea = 7.
    \nso area of each equilateral triangle is 7 sq m.<\/p>\n

    Find the surface area (SA) of the triangular pyramid.
    \nSA = 4T
    \nSA = ______ \u00d7 T
    \nSA = 4 \u00d7 ________
    \n= _______
    \nThe surface area of the triangular pyramid is ________ m2<\/sup><\/p>\n

    Answer:
    \nSA = 4T.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the triangular pyramid is 4T.
    \nSA = 4T.
    \nSA is surface area.
    \n4T = triangular pyramid.
    \n4T = SA.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use a net to help find the surface area of a pyramid.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you find the surface area of a pyramid?<\/p>\n

    Answer:
    \nSurface area = 22 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of a pyramid = SxS + 1\/2bh.
    \nside = 4 x 4.
    \nside = 16.
    \nsurface area = 16 + 1\/2bh.
    \narea = 16 + 1\/2 x 4 x 3.
    \narea = 16 + 1\/2 x 12.
    \narea = 16 + 6.
    \narea = 22 sq cm.<\/p>\n

    Question 2.
    \nLook for Relationships How does finding the area of one face of a triangular pyramid that is made up of equilateral triangles help you find the surface area of the triangular pyramid?
    \nAnswer:<\/p>\n

    Question 3.
    \nMake Sense and Persevere in the formula SA = 47, for the surface area of a triangular pyramid in which the faces are equilateral triangles, what does the variable T represent?<\/p>\n

    Answer:
    \nSurface area = 47.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe surface area of the equilateral triangle = SxS + 1\/2 bh.
    \narea = 4 x 4 + 1\/2 x 5 x 12.
    \narea = 16 + 5 x 6.
    \narea = 16 + 30.
    \narea = 47.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nEach side of the base of a square pyramid is 4 inches and the height of each triangular face is 3 inches. Draw a net for this pyramid and find its surface area.
    \n\"Envision<\/p>\n

    Answer:
    \nThe surface area of the pyramid = 22 sq in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nEach side of the base of a square pyramid is 4 inches and the height of each triangular face is 3 inches.
    \nsurface area = sxs +1\/2bh.
    \nsurface area = 4 x 4 + 1\/2 3 x 4.
    \narea = 16 + 6.
    \narea = 22 sq in.<\/p>\n

    Question 5.
    \nThe faces of this triangular pyramid are equilateral triangles. Draw a net of the pyramid and use it to find the surface area.
    \n\"Envision<\/p>\n

    Answer:
    \nThe surface area of the pyramid = 204.4 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nbases = 12 ft and h = 10.4 ft.
    \nsurface area = sxs +1\/2bh.
    \nsurface area = 12 x 12 + 1\/2 12 x 10.4.
    \narea = 144 +60.4.
    \narea = 204.4 sq ft.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 6 and 7, find the surface area of each pyramid. The faces of each triangular pyramid are equilateral triangles.
    \nQuestion 6.
    \n\"Envision<\/p>\n

    Answer:
    \nThe surface area is 84 sq.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nArea of the base = 7 x 7.
    \narea = 49.
    \nsurface area = 49 + 1\/2 x 7 x 10.
    \narea = 49 + 35.
    \narea = 84.
    \nso the surface area is 84 sq in.<\/p>\n

    Question 7.
    \n\"Envision
    \nAnswer:
    \nThe surface area is 51.2 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nArea of the base = 6 x 6.
    \narea = 36.
    \nsurface area = 36 + 1\/2 x 6 x 5.2.
    \narea = 36 +15.2.
    \narea = 51.2.
    \nso the surface area is 51.2 sq cm.<\/p>\n

    Question 8.
    \nComplete the net at the right to find the surface area of this triangular pyramid. The faces of the pyramid are equilateral triangles.
    \n\"Envision<\/p>\n

    Answer:
    \nThe surface area is 459.6 sq mm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nArea of the base = 18 x 18.
    \narea = 324.
    \nsurface area = 324 + 1\/2 x 18 x 15.6.
    \narea = 324 + 135.6.
    \narea = 459.6.
    \nso the surface area is 459.6 sq mm.<\/p>\n

    Question 9.
    \nSimone is designing a piece of artwork in the shape of a square pyramid for a hotel. She wants to cover the pyramid with decorative glass. How many square feet of glass does Simone need to cover the entire pyramid?
    \n\"Envision<\/p>\n

    Answer:
    \nThe surface area is 35 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nArea of the base = 5 x 5.
    \narea = 25.
    \nsurface area = 25 + 1\/2 x 5 x 4.
    \narea = 25 +10.
    \narea = 35.
    \nso the surface area is 35 sq ft.<\/p>\n

    Question 10.
    \nCritique Reasoning<\/strong> Kurt says that the surface area of this triangular pyramid with faces that are equilateral triangles is 173 cm2. Do you agree with Kurt? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe surface area is 570.3 sq cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nArea of the base = 20 x 20.
    \narea = 400.
    \nsurface area = 400 + 1\/2 x 20 x 17.3.
    \narea = 400 + 170.3.
    \narea = 570.3.
    \nso the surface area is 570.3 sq cm.<\/p>\n

    In 11 and 12, use the pyramid and net shown.
    \n\"Envision
    \nQuestion 11.
    \nModel with Math Ken drew a square pyramid and its net to represent a doghouse that he is building. Complete the net by filling in the missing measures.<\/p>\n

    Answer:
    \nThe surface area is 16.5 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nArea of the base = 3 x 3.
    \narea = 9.
    \nsurface area = 9 + 1\/2 x 3 x 5.
    \narea = 9 + 7.5.
    \narea = 16.5.
    \nso the surface area is 16.5 sq ft.<\/p>\n

    Question 12.
    \nUse the net to find the amount of wood Ken needs to make the doghouse.
    \nAnswer:<\/p>\n

    Question 13.
    \nThe surface area of this square pyramid is 644 ft2<\/sup>. Can the value of x be 20? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe surface area is 336 sq ft.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nArea of the base = 14 x 14.
    \narea = 196.
    \nsurface area = 196 + 1\/2 x 14 x 20.
    \narea = 196 + 140.
    \narea = 336.
    \nso the surface area is 336 sq ft.<\/p>\n

    Question 14.
    \nConstruct Arguments<\/strong> Which of these pyramids do you think has the greater surface area? Explain.<\/p>\n

      \n
    • Square pyramid: The base is 10 cm by 10 cm and the triangular faces have a height of 8.66 cm.<\/li>\n
    • Triangular pyramid: All the faces are equilateral triangles with a base of 10 cm and a height of 8.66 cm.
      \nAnswer:<\/li>\n<\/ul>\n

      Question 15.
      \nHigher Order Thinking<\/strong> The base of a pyramid can be any polygon. How many faces does a pentagonal pyramid have? Describe the shapes of the faces.
      \nAnswer:<\/p>\n

      Question 16.
      \nVocabulary What is the term used to describe a point where three or more edges of a solid figure meet?
      \nAnswer:<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 17.
      \nWhich net represents the pyramid with the greatest surface area?
      \n\"Envision
      \nAnswer:<\/p>\n

      Lesson 7.8 Find Volume with Fractional Edge Lengths<\/h3>\n

      Solve & Discuss It!<\/strong>
      \nA rectangular prism has the dimensions shown. What is the volume of this rectangular prism?<\/p>\n

      I can… find the volume of a rectangular prism with fractional edge lengths.
      \n\"Envision<\/p>\n

      Use Structure
      \nHow might filling the rectangular prism with layers of 3-inch cubes help you find the volume?<\/p>\n

      Focus on math practices
      \nLook for Relationships You know how to use the formula V = \\(\\frac{1}{2}\\)wh to find the volume of a rectangular prism. How might you use the formula to find the volume of the prism above?<\/p>\n

      Essential Question<\/strong>
      \nHow can you find the volume of a rectangular prism with fractional edge lengths?<\/p>\n

      Try It!<\/strong><\/p>\n

      Find the volume of the rectangular prism built from \\(\\frac{1}{2}\\)-inch cubes.
      \n\"Envision
      \nThe bottom layer has _______ cubes. The prism is _______ cubes high. There are a total of _______ cubes in the prism. Each cube has a volume of _______ in3<\/sup>.
      \nVolume of prism = _______ \u00d7 _______ = _______ in3<\/sup>.<\/p>\n

      Answer:
      \nVolume of prism =<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe bottom layer has 5 cubes.
      \nvolume of the rectangular prism = 2(lw) + 2(wh) + 2(lh).
      \nvolume = 2(2.5 x 2.5) + 2(2.5 x 2.5) + 2(2.5 x 2.5).
      \nvolume = 2(
      \nvolume of prism =<\/p>\n

      Convince Me! Suppose that the length of the rectangular prism in the Try It! were 3\\(\\frac{1}{2}\\) inches instead of 2\\(\\frac{1}{2}\\) inches. How many cubes would there be in the prism? What would be the volume of the prism?<\/p>\n

      Try It!<\/strong><\/p>\n

      Find the volume of each rectangular prism.
      \na.
      \n\"Envision<\/p>\n

      Answer:
      \nThe volume of rectangular prism = 61 sq cm.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nl = 3.2 cm, h = 4.5 cm, and w = 2.8 cm.
      \nvolume of rectangular prism = 2(lw) + 2(wh) + 2(lh).
      \nvolume = 2(3.2 x 2.8) + 2(2.8 x 4.5) + 2(3.2 x 4.5).
      \nvolume = 2(3.5) + 2(12.6) + 2(14.4).
      \nvolume = 7 + 25.2 + 28.8.
      \nvolume = 61 sq cm.<\/p>\n

      b.
      \n\"Envision
      \nAnswer:
      \nThe volume of rectangular prism = 121.5 sq ft.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nl = 4.5 cm, h = 4.5 cm, and w = 4.5 cm.
      \nvolume of rectangular prism = 2(lw) + 2(wh) + 2(lh).
      \nvolume = 2(4.5 x 4.5) + 2(4.5 x 4.5) + 2(4.5 x 4.5).
      \nvolume = 2(20.25) + 2(20.25) + 2(20.25).
      \nvolume = 40.5 + 40.5 + 40.5.
      \nvolume = 121.5 sq ft.<\/p>\n

      KEY CONCEPT<\/strong>
      \nYou can find the volume of a rectangular prism with fractional edge lengths by determining the number of same-sized cubes with unit fraction edge lengths needed to completely fill the prism, then multiplying that number of cubes by the volume of each cube. You can also apply a formula.
      \n\"Envision<\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nEssential Question<\/strong> How can you find the volume of a rectangular prism with fractional edge lengths?<\/p>\n

      Answer:
      \nThe volume of a rectangular prism = l x w x h.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of a rectangular prism = l x w x h.
      \nwhere l = length.
      \nw = width.
      \nh = height.<\/p>\n

      Question 2.
      \nHow is finding the volume of a rectangular prism with fractional edge lengths similar to finding the volume of a rectangular prism with whole number edge lengths?<\/p>\n

      Answer:
      \nThe volume of a rectangular prism = l x w x h.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of a rectangular prism = l x w x h.
      \nwhere l = length.
      \nw = width.
      \nh = height.<\/p>\n

      Question 3.
      \nConstruct Arguments How can you use the number of \\(\\frac{1}{2}\\)-inch cubes in a rectangular prism to find the number of unit cubes in the rectangular prism?<\/p>\n

      Answer:
      \nThe volume of a rectangular prism = 0.125 sq in.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of a rectangular prism = l x w x h.
      \nwhere l = length.
      \nw = width.
      \nh = height.
      \nvolume = 0.5 x 0.5 x 0.5.
      \nvolume = 0.125 sq in.<\/p>\n

      Do You Know How?<\/strong>
      \nIn 4 and 5, tell how many of each size of cube can fill a 1-inch cube.
      \nQuestion 4.
      \nEdge = \\(\\frac{1}{3}\\) inch<\/p>\n

      Answer:
      \nVolume = 0.027 cubic in.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nedge = 1\/3 in.
      \nvolume = ax ax a.
      \nvolume = 0.3 x 0.3 x 0.3.
      \nvolume = 0.027 cubic in.<\/p>\n

      Question 5.
      \nEdge = \\(\\frac{1}{4}\\) inch<\/p>\n

      Answer:
      \nVolume = 0.027 cubic in.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nedge = 1\/4 in.
      \nvolume = ax ax a.
      \nvolume = 0.25 x 0.25 x 0.25.
      \nvolume = 0.75 cubic in.<\/p>\n

      In 6-9, find the volume of each rectangular prism.
      \nQuestion 6.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 4.5 cubic in.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nl = 3\/2 in, w = 3\/2 in, and h = 3\/2 in.
      \nvolume = ax ax a.
      \nvolume = 1.5 x 1.5 x 1.5.
      \nvolume = 4.5 cubic in.<\/p>\n

      Question 7.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 233.1 cubic m.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of the rectangular prism = lwh.
      \nlength = 14.8 m.
      \nwidth = 4.5 m.
      \nheight = 3.5 m.
      \nvolume = 14.8 x 4.5 x 3.5.
      \nvolume = 233.1 cubic m.<\/p>\n

      Question 8.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 3.75 cubic ft.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of the rectangular prism = lwh.
      \nlength = 1.25 ft.
      \nwidth = 1.25 ft.
      \nheight = 2 ft.
      \nvolume = 1.25 x 1.25 x 1.25.
      \nvolume = 3.75 cubic ft.<\/p>\n

      Question 9.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 12.167 cubic cm.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of the rectangular prism = lwh.
      \nlength = 2.3 cm.
      \nwidth = 2.3 cm.
      \nheight = 2.3 cm.
      \nvolume = 2.3 x 2.3 x 2.3.
      \nvolume = 12.167 cubic cm.<\/p>\n

      Practice & Problem Solving<\/strong><\/p>\n

      In 10-13, find the volume of each rectangular prism.
      \nQuestion 10.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 31.2 cubic m.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of the rectangular prism = lwh.
      \nlength = 6.5 m.
      \nwidth = 4 m.
      \nheight = 1.2 m.
      \nvolume = 6.5 x 4 x 1.2.
      \nvolume = 31.2 cubic m.<\/p>\n

      Question 11.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 3.75 cubic yd.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of the rectangular prism = lwh.
      \nlength = 2 yd.
      \nwidth = 1.6 yd.
      \nheight = 5.3 yd.
      \nvolume = 2 x 1.6 x 5.3.
      \nvolume = 16.96 cubic yd.<\/p>\n

      Question 12.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 35.937 cubic ft.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of the rectangular prism = lwh.
      \nlength = 3.3 ft.
      \nwidth = 3.3 ft.
      \nheight =\u00a0 3.3 ft.
      \nvolume = 3.3 x 3.3 x 3.3.
      \nvolume = 35.937 cubic ft.<\/p>\n

      Question 13.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 1.512 cubic m.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of the rectangular prism = lwh.
      \nlength = 0.7 m.
      \nwidth = 0.9 m.
      \nheight = 2.4 m.
      \nvolume = 0.7 x 0.9 x 2.4.
      \nvolume = 1.512 cubic m.<\/p>\n

      Question 14.
      \nA clear box has the shape of a rectangular prism and is filled with sand. Find the volume of the box.
      \n\"Envision<\/p>\n

      Answer:
      \nVolume = 241.3 cubic in.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe volume of the rectangular prism = lwh.
      \nlength = 8.25 in.
      \nwidth = 4.5 in.
      \nheight = 6.5 in.
      \nvolume = 8.25 x 4.5 x 6.5.
      \nvolume = 241.3 cubic in.<\/p>\n

      Question 15.
      \nUse Structure A rectangular prism has a length of 2\\(\\frac{1}{2}\\) yd, a width of 1\\(\\frac{1}{2}\\) yd, and a height of 1\\(\\frac{1}{2}\\) yd. You use cubes with fractional edge lengths of \\(\\frac{1}{2}\\) yd to find the volume. How many cubes are t\u0127ere for each of the length, width, and height of the prism? What is the volume of the prism?<\/p>\n

      Answer:
      \nThe volume of the prism = 5.625 cubic yd.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA rectangular prism has a length of 2\\(\\frac{1}{2}\\) yd, a width of 1\\(\\frac{1}{2}\\) yd, and a height of 1\\(\\frac{1}{2}\\) yd.
      \nvolume of the prism = l x w x h.
      \nl = 2.5, w = 1.5, and h = 1.5.
      \nvolume = 2.5 x 1.5 x 1.5.
      \nvolume = 5.625 cubic yd.<\/p>\n

      Question 16.
      \nA gift box has the shape of a cube. The length of each side is 10.5 cm. What is the volume of the gift box?<\/p>\n

      Answer:
      \nThe volume of the gift box = 31.5 cubic cm.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA gift box has the shape of a cube.
      \nthe length of each side is 10.5 cm.
      \nvolume = lx w x h.
      \nvolume = 10.5 x 10.5 x 10.5.
      \nvolume = 31.5.
      \nso the volume of the gift box = 31.5 cubic cm.<\/p>\n

      Question 17.
      \nA school locker has a length of 1 ft, a width of 18 in., and a height of 2\\(\\frac{1}{2}\\) ft. What is the volume of the locker in cubic feet?
      \n\"Envision<\/p>\n

      Answer:
      \nThe volume of rectangular prism = 45 cubic ft.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA school locker has a length of 1 ft, a width of 18 in, and a height of 2(1\/2).
      \nvolume of the prism = l x w x h.
      \nvolume = 1 x 18 x 2.5.
      \nvolume = 45 cubic ft.<\/p>\n

      In 18 and 19, use the table.
      \n\"Envision
      \nQuestion 18.
      \nUse Structure Sandy has two boxes with the dimensions shown. She wants to use the box with the greater volume to ship a gift to her friend. Which box should Sandy use? Explain.<\/p>\n

      Answer:
      \nSandy ship a box B.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nSandy has two boxes with the dimensions shown.
      \nthe volume of the Box A = l x w x h.
      \nvolume = 7.5 x 2 x 11.5.
      \nvolume = 172.5 cubic ft.
      \nvolume = 172.5 cubic ft.
      \nthe volume of the Box B = l x w x h.
      \nvolume = 9 x 2.5 x 8.5.
      \nvolume = 191.25 cubic ft.<\/p>\n

      Question 19.
      \nSandy finds a third box, box C, that has a length of 8 inches, a width of 2\\(\\frac{3}{4}\\) inches, and a height of 10\\(\\frac{1}{2}\\) inches. If Sandy wants to use the box with the greatest volume, should she use box C? Explain.<\/p>\n

      Answer:
      \nSandy will ship box C.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nSandy finds a third box, box C, that has a length of 8 inches, a width of 2\\(\\frac{3}{4}\\) inches, and a height of 10\\(\\frac{1}{2}\\) inches.
      \nvolume = l x w x h.
      \nvolume = 8 x 11\/4 x 21\/2.
      \nvolume = 8 x 2.75 x 10.5.
      \nvolume = 231 cubic in.
      \nSandy will ship box C.<\/p>\n

      Question 20.
      \nThe volume of a large crate is 84 yd3<\/sup>. It is 2\\(\\frac{2}{3}\\) yd wide and 4\\(\\frac{2}{3}\\) yd high. What is the length of the crate?<\/p>\n

      Answer:
      \nThe length of the crate = 7.023.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe volume of a large crate is 84 yd3<\/sup>.
      \nIt is 2\\(\\frac{2}{3}\\) yd wide and 4\\(\\frac{2}{3}\\) yd high.
      \nv = l x w x h.
      \n84 = l x 8\/3 x 14\/3.
      \n84 = l x 2.6 x 4.6.
      \n84 = l x 11.96.
      \nl = 84\/11.96.
      \nl = 7.023.
      \nso the length of the crate = 7.023 sq yds.<\/p>\n

      Question 21.
      \nHigher Order Thinking<\/strong> A box covers an area of 8\\(\\frac{3}{4}\\) in.2<\/sup> when resting on its base. The volume of the box is 74\\(\\frac{3}{8}\\) in.3<\/sup>. Can you find the surface area of the box? Explain.<\/p>\n

      Answer:
      \nThe surface area of the box = 74.375 cubic in.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA box covers an area of 8\\(\\frac{3}{4}\\) in.2<\/sup> when resting on its base.
      \nThe volume of the box is 74\\(\\frac{3}{8}\\) in.3<\/sup>
      \nThe surface area of the box = 595\/8.
      \nthe surface area of the box = 74.375 cubics in.<\/p>\n

      Question 22.
      \nMake Sense and Persevere A gold bar is similar in shape to a rectangular prism. A standard mint bar is approximately 7 in. \u00d7 3\\(\\frac{5}{8}\\) in. \u00d7 1\\(\\frac{3}{4}\\) in. If the value of gold is $1,313 per ounce, about how much is one gold bar worth? Use the formula w\u224811.15n, where w is the weight in ounces and n is the volume in cubic inches, to find the weight in ounces. Explain how you found your answer.
      \n\"Envision
      \nAnswer:<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 23.
      \nWhich rectangular prism with the given dimensions has the same volume as the prism shown?
      \n\"Envision
      \nA. 1 in., 3.5 in., 4.25 in.
      \nB. 1.25 in., 3.5 in., 4 in.
      \nC. 1.75 in., 3 in., 3.5 in.
      \nD. 2 in., 2.25 in., 4 in.<\/p>\n

      Answer:
      \nOption C is correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nvolume of the rectangular prism = l x w x h.
      \nvolume = 4 x 7\/4 x 5\/2.
      \nvolume = 4 x 1.75 x 2.5.
      \nvolume = 17.5.
      \nso option C is correct.<\/p>\n

      Topic 7 Review<\/h3>\n

      Topic Essential Question<\/strong>
      \nHow can the areas of certain shapes be found? What are the meanings of surface area and volume and how can surface area and volume be found?<\/p>\n

      Vocabulary Review
      \nWrite the vocabulary term that best represents each item.
      \nVocabulary<\/p>\n

        \n
      • net<\/li>\n
      • rhombus<\/li>\n
      • trapezoid<\/li>\n
      • vertex<\/li>\n
      • volume<\/li>\n<\/ul>\n

        Question 1.
        \nThe measure of the space this solid figure occupies.
        \n\"Envision<\/p>\n

        Answer:
        \nThe measure of the space this solid figure occupies is volume.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe measure of the space this solid figure occupies is volume.
        \nthe volume of the prism = l x w x h.
        \nwhere l = length.
        \nw = width.
        \nh = height.<\/p>\n

        Question 2.
        \n\"Envision<\/p>\n

        Answer:
        \nThe measure of the space this solid figure occupies is net.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe measure of the space this solid figure occupies is net.<\/p>\n

        Question 3.
        \n\"Envision
        \nAnswer:
        \nThe figure is a rhombus.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe figure is a rhombus.
        \nfor example:
        \nthe volume of the rhombus = 12 ABH.
        \nwhere a and b are diagonals of the rhombus.
        \nh is the height of the prism.<\/p>\n

        Question 4.
        \n\"Envision
        \nAnswer:
        \nThe figure is a trapezoid.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe figure is a trapezoid.
        \narea of the trapezoid = a+b\/2 h.
        \nwhere a = base.
        \nb = base.
        \nh = height.
        \nso the figure is a trapezoid.<\/p>\n

        Use Vocabulary in Writing
        \nDescribe how to find the area of the quadrilateral. Use vocabulary words in your explanation.
        \n\"Envision<\/p>\n

        Answer:
        \nArea = 44 sq cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the quadrilateral = 1\/2 x diagonals length x (sum of the height of two triangles).
        \narea = 1\/2 x 11 x 8.
        \narea = 44 sq cm.<\/p>\n

        Concepts and Skills Review<\/strong><\/p>\n

        Lesson 7.1 Find Areas of Parallelograms and Rhombuses<\/strong><\/p>\n

        Quick Review<\/strong>
        \nYou can use the formula A = bh to find the area of a parallelogram or a rhombus.<\/p>\n

        Example<\/strong>
        \nFind the area of the parallelogram.
        \n\"Envision
        \nA = bh
        \nA = 12 \u00d7 8
        \nA = 96
        \nThe area of the parallelogram is 96 ft2<\/sup>.<\/p>\n

        Practice<\/strong>
        \nIn 1-4, find the area of each parallelogram or rhombus.
        \nQuestion 1.
        \n\"Envision<\/p>\n

        Answer:
        \nArea = 36 sq m.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the parallelogram = bh.
        \nwhere b = base and h = height.
        \narea = 4 x 9.
        \narea = 36 sq m.<\/p>\n

        Question 2.
        \n\"Envision<\/p>\n

        Answer:
        \nArea = 63.2 sq cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the parallelogram = bh.
        \nwhere b = base and h = height.
        \narea = 8 x 7.9.
        \narea = 63.2 sq cm.<\/p>\n

        Question 3.
        \nRhombus
        \nb = 14 in.
        \nh = 9 in.<\/p>\n

        Answer:
        \nArea = 126 sq in.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the parallelogram = bh.
        \nwhere b = base and h = height.
        \narea = 14 x 9.
        \narea = 126 sq in.<\/p>\n

        Question 4.
        \nParallelogram
        \nb = 12 ft
        \nh = 8.5 ft<\/p>\n

        Answer:
        \nArea = 102 sq ft.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the parallelogram = bh.
        \nwhere b = base and h = height.
        \narea = 12 x 8.5.
        \narea = 102 sq ft.<\/p>\n

        Question 5.
        \nA rhombus has an area of 375 mm2<\/sup> and a base of 25 mm. What is its height?<\/p>\n

        Answer:
        \nheight = 15 sq mm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the parallelogram = bh.
        \nwhere b = base and h = height.
        \narea = 375 sq mm.
        \nbase = 25 mm.
        \n375 = 25h.
        \nh = 375\/25.
        \nh = 15 sqmm.<\/p>\n

        Lesson 7.2 Solve Triangle Area Problems<\/strong><\/p>\n

        Quick Review<\/strong>
        \nYou can use the formula A = \\(\\frac{1}{2}\\)bh to find the area of any triangle.<\/p>\n

        Example<\/strong>
        \nFind the area of the triangle.
        \n\"Envision
        \nA = \\(\\frac{1}{2}\\) \u00d7 (26 \u00d7 20)
        \nA = 260 cm2<\/sup><\/p>\n

        Practice<\/strong>
        \nFind the area of each triangle.
        \nQuestion 1.
        \n\"Envision<\/p>\n

        Answer:
        \nArea of the triangle = 5 sq yd.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the triangle = 1\/2 bh.
        \narea = 1\/2 x 2 x 5.
        \narea = 5.<\/p>\n

        Question 2.
        \n\"Envision
        \nAnswer:
        \nArea of the triangle = 24 sq ft.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the triangle = 1\/2 bh.
        \narea = 1\/2 x 8 x 6.
        \narea = 4 x 6.
        \narea = 24 sq ft.<\/p>\n

        Question 3.
        \nb = 12.4 cm
        \nh = 18 cm<\/p>\n

        Answer:
        \nArea of the triangle = 111.6 sq cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the triangle = 1\/2 bh.
        \narea = 1\/2 x 12.4 x 18.
        \narea = 12.4 x 9.
        \narea = 111.6 sq cm.<\/p>\n

        Question 4.
        \nb = 3.5 m
        \nh = 6 m<\/p>\n

        Answer:
        \nArea of the triangle = 10.5 sq m.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the triangle = 1\/2 bh.
        \narea = 1\/2 x 3.5 x 6.
        \narea = 3 x 3.5.
        \narea = 10.5 sq m.<\/p>\n

        Lesson 7.3 Find Areas of Trapezoids and Kites<\/strong><\/p>\n

        Quick Review<\/strong>
        \nYou can find the area of a trapezoid by decomposing it into a rectangle and one or more triangles. You can find the area of a kite by decomposing it into triangles.<\/p>\n

        Example<\/strong>
        \nFind the area of the trapezoid and the kite.
        \n\"Envision<\/p>\n

        Practice<\/strong>
        \nFind the area of each trapezoid or kite.
        \nQuestion 1.
        \n\"Envision<\/p>\n

        Answer:
        \nArea of the trapezoid = 32.5 sq cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nbase = 5 cm.
        \nh = 11 cm.
        \narea of the triangle = 1\/2(1 x 5).
        \narea = 5\/2 = 2.5.
        \narea of the rectangle = 5 x 6.
        \narea = 30.
        \narea of the trapezoid = 2.5 + 30.
        \narea = 32.5 sq cm.<\/p>\n

        Question 2.
        \n\"Envision
        \nAnswer:
        \nArea of the trapezoid = 96 sq m.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the triangle = 1\/2(7 x 12).
        \narea = 42.
        \narea of the rectangle = 1 x 12.
        \narea = 12.
        \narea of the trapezoid = 42 + 42 + 12.
        \narea = 96 sq m.<\/p>\n

        Question 3.
        \n\"Envision<\/p>\n

        Answer:
        \nArea = 48 sq in.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the kite = 1\/2[(8 x 4) x 4].
        \narea = 1\/2[12] x 4.
        \narea = 24.
        \narea of the kite = 24 + 24.
        \narea = 48 sq in.<\/p>\n

        Question 4.
        \n\"Envision<\/p>\n

        Answer:
        \nArea of the kite = 80 sq in.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \narea of the kite = 1\/2[(10 x 4) x 2].
        \narea = 1\/2[40] x 2.
        \narea = 20 x 2.
        \narea = 40.
        \narea of the kite = 40 + 40.
        \narea = 80 sq in.<\/p>\n

        Lesson 7.4 Find Areas of Polygons<\/strong><\/p>\n

        Quick Review<\/strong>
        \nTo find the area of a polygon, you can decompose or compose shapes, then use addition or subtraction to calculate the area.<\/p>\n

        Example<\/strong>
        \nFind the area of the polygon.
        \n\"Envision
        \nArea = (3 \u00d7 5) + (10 \u00d7 4) + (4 \u00d7 10)
        \n= 15 + 40 + 40 = 95
        \nThe area of the polygon is 95 yd2<\/sup>.<\/p>\n

        Practice<\/strong>
        \nQuestion 1.
        \nFind the area of the polygon.
        \n\"Envision
        \nAnswer:
        \nArea of the polygon = -27.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe area of the polygon = (2 x -6) + (-3 x -5).
        \narea of the polygon = (-12) + (-15).
        \narea = -12 – 15.
        \narea = -27.
        \nso the area of the polygon = -27.<\/p>\n

        Lesson 7.5 Represent Solid Figures Using Nets<\/strong><\/p>\n

        Quick Review<\/strong>
        \nYou can use nets to represent solid figures.<\/p>\n

        Example<\/strong>
        \nClassify the solid figure and draw a net to represent it.
        \n\"Envision
        \nThis figure has two congruent parallel bases, so it is a prism. The bases are rectangles, so it is a rectangular prism.
        \nNet of rectangular prism:
        \n\"Envision<\/p>\n

        Practice<\/strong>
        \nIn 1 and 2, classify the solid figures
        \nQuestion 1.
        \n\"Envision<\/p>\n

        Answer:
        \nThe figure name is a triangular pyramid.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe above figure is a triangular pyramid.
        \nthe surface area of triangular pyramid = 1\/2(a x b) + 3\/2(b x s).
        \nwhere b = base.
        \ns = side.<\/p>\n

        Question 2.
        \n\"Envision<\/p>\n

        Answer:
        \nThe figure name is a triangular pyramid.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe above figure is a triangular pyramid.
        \nthe surface area of triangular pyramid = 1\/2(a x b) + 3\/2(b x s).
        \nwhere b = base.
        \ns = side.<\/p>\n

        Question 3.
        \nDraw a net of the pyramid shown.
        \n\"Envision
        \nAnswer:<\/p>\n

        In 4 and 5, identify each solid from its net.
        \nQuestion 4.
        \n\"Envision<\/p>\n

        Answer:
        \nThe net of the solid is a square pyramid.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe net of the solid is a square pyramid.
        \nthe formula of square pyramid = 1\/3 x bxb x h.
        \nwhere b = base, and h = height.
        \nthe figure is a square pyramid.<\/p>\n

        Question 5.
        \n\"Envision<\/p>\n

        Answer:
        \nThe net of the solid is a rectangular pyramid.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe net of the solid is a rectangular pyramid.
        \nthe formula of rectangular pyramid = 1\/3 x l x w x h.
        \nwhere l = length, w = width, and h = height.
        \nthe figure is a rectangular pyramid.<\/p>\n

        Lesson 7.6 Find Surface Areas of Prisms<\/strong><\/p>\n

        Quick Review<\/strong>
        \nYou can use a net or a formula to find the surface area of a prism.<\/p>\n

        Example<\/strong>
        \nFind the surface area.
        \n\"Envision<\/p>\n

        Practice<\/strong>
        \nFind the surface area of each prism.
        \nQuestion 1.
        \n\"Envision<\/p>\n

        Answer:
        \nThe surface area of the rectangular prism = 126 cubic ft.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nl = 6 ft, w = 3 ft, and h = 5 ft.
        \nsurface area of rectangular prism = 2(lw + lh + hw).
        \narea = 2(6 x 3) + (6 x 5) + (5 x 3).
        \narea = 2(18) + 30 + 15.
        \narea = 2(63).
        \narea = 126.<\/p>\n

        Question 2.
        \n\"Envision
        \nAnswer:
        \nThe surface area of the triangular pyramid = 7168 cubic cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nthe surface area of the triangular prism = a x b x c x h.
        \nwhere a = base side.
        \nb = base side.
        \nc = base side.
        \nh = height.
        \nsurface area of the triangular prism = 8 x 16 x 8 x 7.
        \narea = 7168 cubic cm.<\/p>\n

        Question 3.
        \nCube
        \ns = 9.4 m<\/p>\n

        Answer:
        \nArea = 530.16 sq m.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \ns = 9.4 m.
        \nThe surface area of a cube is 6a square.
        \narea = 6 x 9.4 x 9.4.
        \narea = 6 x 88.36.
        \narea = 530.16 sq m.<\/p>\n

        Question 4.
        \nCube
        \ns = 7 cm<\/p>\n

        Answer:
        \nArea = 294 sq cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \ns = 9.4 m.
        \nThe surface area of a cube is 6a square.
        \narea = 6 x 7 x 7.
        \narea = 6 x 49.
        \narea = 294 sq cm.<\/p>\n

        Question 5.
        \nRectangular prism
        \nl = 12 in.
        \nw = 7 in.
        \nh = 3 in.<\/p>\n

        Answer:
        \nThe surface area of the rectangular prism = 282 cubics in.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nl = 12 in, w = 7 in, and h = 3 in.
        \nsurface area of rectangular prism = 2(lw + lh + hw).
        \narea = 2(12 x 7) + (7 x 3) + (12 x 3).
        \narea = 2(84) + 21 + 36.
        \narea = 2(141).
        \narea = 282.<\/p>\n

        Question 6.
        \nRectangular prism
        \nl = 5 cm
        \nw = 6 cm
        \nh = 7 cm<\/p>\n

        Answer:
        \nThe surface area of the rectangular prism = 214 cubics cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nl = 5 cm, w = 6 cm, and h = 7 cm.
        \nsurface area of rectangular prism = 2(lw + lh + hw).
        \narea = 2(5 x 6) + (7 x 6) + (5 x 7).
        \narea = 2(30) + 42 + 35.
        \narea = 2(107).
        \narea = 214.<\/p>\n

        Lesson 7.7 Find Surface Areas of Pyramids<\/strong><\/p>\n

        Quick Review<\/strong>
        \nYou can use a net or a formula to find the surface area of a pyramid.<\/p>\n

        Example<\/strong>
        \nFind the surface area.
        \nArea of one triangle:
        \n\"Envision
        \nT = \\(\\frac{1}{2}\\) \u00d7 10 \u00d7 8.7 = 43.5
        \nSA = 4T
        \n= 4 \u00d7 43.5
        \n= 174
        \nThe surface area of the pyramid is 174 m2<\/sup>.<\/p>\n

        Practice<\/strong>
        \nIn 1 and 2, find the surface area of each pyramid.
        \nQuestion 1.
        \n\"Envision<\/p>\n

        Answer:
        \nThe surface area of the pyramid = 10 sq in.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nbases = 4 in.
        \nheight = 5 in.
        \nsurface area of the pyramid = 1\/2 (p x s).
        \narea = 1\/2 (4 x 5).
        \narea = 1\/2(20).
        \narea = 10 sq in.<\/p>\n

        Question 2.
        \n\"Envision
        \nAnswer:
        \nThe surface area of the pyramid = 21.35 sq cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nbases = 7 cm.
        \nheight = 6.1 cm.
        \nsurface area of the pyramid = 1\/2 (p x s).
        \narea = 1\/2 (7 x 6.1).
        \narea = 1\/2(42.7).
        \narea = 21.35 sq cm.<\/p>\n

        Question 3.
        \nEach side of the base of a square pyramid is 10 ft and the height of each triangular face is 7 ft. Find the surface area of the pyramid.<\/p>\n

        Answer:
        \nThe surface area of the pyramid = 607 sq ft.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nEach side of the base of a square pyramid is 10 ft and the height of each triangular face is 7ft.
        \nsurface area of the pyramid = axa + 2a \u221aaxa\/4 + h x h.
        \nwhere a = base edge.
        \nh = height.
        \narea = 100+ 20 \u221a100\/4 + 49.
        \narea = 120 \u221a25 + 49.
        \narea = 120 x 5 + 7.
        \narea = 600 + 7.
        \narea = 607.<\/p>\n

        Lesson 7.8 Find Volume with Fractional Edge Lengths<\/strong><\/p>\n

        Quick Review<\/strong>
        \nThe volume of a rectangular prism is equal to the area of the base multiplied by the height.<\/p>\n

        Example<\/strong>
        \nFind the volume of the rectangular prism.
        \n\"Envision
        \nSTEP 1 Find the number of small \\(\\frac{1}{4}\\)-in. cubes that will fill the prism.
        \n14 small \\(\\frac{1}{4}\\)-in. cubes 31in. fit along the 3\\(\\frac{1}{2}\\) in. side.
        \n12 small \\(\\frac{1}{4}\\)-in. cubes fit along the 3 in. side.
        \n15 small \\(\\frac{1}{4}\\)-in. cubes fit along the 3\\(\\frac{3}{4}\\) in. side.
        \n14 \u2022 12 \u2022 15 = 2,520 small \\(\\frac{1}{4}\\)-in. cubes fill the prism.<\/p>\n

        STEP 2
        \nFind the volume of each small 7-in. cube.
        \nV = lwh = \\(\\frac{1}{4}\\) in. \u2022 \\(\\frac{1}{4}\\) in. \u2022 \\(\\frac{1}{4}\\) in. = \\(\\frac{1}{64}\\) in.3<\/sup><\/p>\n

        STEP 3
        \nFind the volume of the prism.
        \n2,520 \u2022 \\(\\frac{1}{64}\\) in.3<\/sup> = 39\\(\\frac{3}{8}\\) in.3<\/sup>
        \nYou can also use a formula. .
        \nV = lwh = 3\\(\\frac{1}{2}\\) in. \u00d7 3 in. \u00d7 3\\(\\frac{3}{4}\\) in. = 39\\(\\frac{3}{8}\\) in.3<\/sup><\/p>\n

        Practice<\/strong>
        \nFind the volume of each rectangular prism.
        \nQuestion 1.
        \n\"Envision<\/p>\n

        Answer:
        \nVolume = 777.45 cubic in.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nvolume of rectangular prism = l x w x h.
        \nwhere l = 5 in, w = 22\/3 in, and h = 64\/3 in.
        \nv = 5 x 7.3 x 21.3.
        \nv = 777.45 cubic in<\/p>\n

        Question 2.
        \n\"Envision<\/p>\n

        Answer:
        \nVolume = 234 cubic ft.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nvolume of rectangular prism = l x w x h.
        \nwhere l = 8 ft, w = 4.5 ft, and h = 6.5 ft.
        \nv = 8 x 4.5 x 6.5.
        \nv = 234 cubic ft.<\/p>\n

        Question 3.
        \n\"Envision<\/p>\n

        Answer:
        \nVolume = 222.794 cubic cm.<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nvolume of rectangular prism = l x w x h.
        \nwhere l = 14.3 cm, w = 3.8 cm, and h = 4.1 cm.
        \nv = 14.3 x 3.8 x 4.1.
        \nv = 222.794 cubic cm.<\/p>\n

        Topic 7 Fluency Practice<\/h3>\n

        Hidden Clue<\/strong>
        \nFor each ordered pair, simplify the two coordinates. Then locate and label the corresponding point on the graph. Draw line segments to connect the points in alphabetical order. Connect L to E to complete the picture, then use the completed picture to help answer the riddle below.
        \nI can… multiply and divide multidigit decimals.
        \n\"Envision
        \n\"Envision<\/p>\n

        Answer:
        \nA: (1.86, 2).
        \nB: (2.4, 0.8).
        \nC: (3.6, 1.25).
        \nD: (5.4, 4.76).
        \nE: (7.2, 8.2).
        \nF: (13.6, 5).
        \nG: (13.1, 8.8).
        \nH: (11.8, 10.5).
        \nI: (9.6, 12.7).
        \nJ: (6.4, 13.2).
        \nK: (4.1, 13.2).
        \nL: (1, 11.5).<\/p>\n

        Explanation:
        \nIn the above-given question,
        \ngiven that,
        \nmultiply and divide the numbers.
        \nA: (1.2 x 1.55, 2.7\/1.35).
        \n(1.86, 2).
        \nB: (1.25 x 1.92, 0.48\/0.6).
        \n(2.4, 0.8).
        \nC: (5.04\/1.4, 0.5 x 2.5).
        \n(3.6, 1.25).
        \nD: (2.16 x 2.5, 11.9\/2.5).
        \n(5.4, 4.76).
        \nE: (16.56\/ 2.3, 5.125 x 1.6).
        \n(7.2, 8.2).
        \nF: (6.12\/0.45, 6.25 x 0.8).
        \n(13.6, 5).
        \nG: (2.62 x 5, 12.32\/1.4).
        \n(13.1, 8.8).
        \nH: (29.5 x 0.4, 3.675 \/0.35).
        \n(11.8, 10.5).
        \nI: (12.48\/1.3, 10.16 x 1.25)
        \n(9.6, 12.7).
        \nJ: (20 x 0.32, 59.4\/4.5).
        \n(6.4, 13.2).
        \nK: (7.79\/1.9, 40 x 0.33).
        \n(4.1, 13.2).
        \nL: (25 x 0.04, 48.3\/4.2).
        \n(1, 11.5).<\/p>\n","protected":false},"excerpt":{"rendered":"

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