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Transcript of NYS COMMON CORE MATHEMATICS answers are below. ... NYS COMMON CORE MATHEMATICS CURRICULUM 6•5...

  • Lesson 1: The Area of Parallelograms Through Rectangle Facts Date: 1/29/14

    S.3

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    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 1

    Problem Set Draw and label the height for each parallelogram.

    1.

    2.

    Calculate the area of each parallelogram. The figures are not drawn to scale.

    3.

    6 cm

    13 cm

    8 cm

    base

    base

    Lesson Summary

    The formula to calculate the area of a parallelogram is = , where represents the base and represents the height of the parallelogram.

    The height of a parallelogram is the line segment perpendicular to the base.

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  • Lesson 1: The Area of Parallelograms Through Rectangle Facts Date: 1/29/14

    S.4

    2014 Common Core, Inc. Some rights reserved. commoncore.org

    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 1

    4.

    5.

    6.

    7. Brittany and Sid were both asked to draw the height of a parallelogram. Their answers are below.

    Brittany Sid

    Are both Brittany and Sid correct? If not, who is correct? Explain your answer.

    base

    height

    base

    height

    5 14 in.

    3 56 in.

    7 23 in.

    2 12 in.

    1.2 ft.

    13.4 ft. 12.8 ft.

    3 12 m

    3 56 m 413 m

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  • Lesson 1: The Area of Parallelograms Through Rectangle Facts Date: 1/29/14

    S.5

    2014 Common Core, Inc. Some rights reserved. commoncore.org

    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 1

    8. Do the rectangle and parallelogram below have the same area? Explain why or why not.

    9. A parallelogram has an area of 20.3 square centimeters and a base of 2.5 centimeters. Write an equation that relates the area to the base and height, . Solve the equation to determine the length of the height.

    15 ft.

    8 ft. 8 ft.

    15 ft.

    10 ft.

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  • Lesson 2: The Area of Right Triangles Date: 1/29/14

    S.9

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    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 2

    Problem Set Calculate the area of each right triangle below. Each figure is not drawn to scale.

    1.

    2.

    3.

    4.

    9.1 cm

    31.2 cm

    32.5 cm

    3 34 km

    5 km

    6 14 km

    61 mm

    60 mm 11 mm

    5 in.

    2.4 in.

    3.2 in.

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  • Lesson 2: The Area of Right Triangles Date: 1/29/14

    S.10

    2014 Common Core, Inc. Some rights reserved. commoncore.org

    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 2

    5.

    6. Elania has two congruent rugs at her house. She cut one vertically down the middle, and she cut diagonally through

    the other one.

    After making the cuts, which rug (labeled A, B, C, or D) has the larger area? Explain.

    7. Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know.

    8. If the area of a right triangle is 916

    sq. ft. and the height is 34

    in., write an equation that relates the area to the base, ,

    and the height. Solve the equation to determine the base.

    16 23 ft.

    10 ft.

    13 13 ft.

    A B

    C

    D

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  • Lesson 3: The Area of Acute Triangles Using Height and Base Date: 1/29/14

    S.13

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    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 3

    Problem Set Calculate the area of each shape below. Figures are not drawn to scale.

    1.

    2.

    3.

    4.

    5 ft.

    12 ft.

    13 ft. 13 ft. 12 ft.

    12 ft. 5 ft.

    4.4 in.

    3.3 in. 6.1 in.

    5.5 in.

    8 m

    14 m

    16 m

    16 m

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  • Lesson 3: The Area of Acute Triangles Using Height and Base Date: 1/29/14

    S.14

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    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 3

    5. Immanuel is building a fence to make an enclosed play area for his dog. The enclosed area will be in the shape of a triangle with a base of 48 in. and an altitude of 32 in. How much space does the dog have to play?

    6. Chauncey is building a storage bench for his sons playroom. The storage bench will fit into the corner and then go along the wall to form a triangle. Chauncey wants to buy a cover for the bench.

    If the storage bench is 2 12 ft. along one wall and 414 ft. along the other wall, how big will the cover

    have to be in order to cover the entire bench?

    7. Examine the triangle to the right. a. Write an expression to show how you would calculate the area.

    b. Identify each part of your expression as it relates to the triangle.

    8. A triangular room has an area of 32 12 sq. m. If the height is 712 m, write an equation to determine the length of the

    base, , in meters. Then solve the equation.

    5 in.

    3 in.

    4 in.

    7 in.

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  • Lesson 4: The Area of Obtuse Triangles Using Height and Base Date: 1/29/14

    S.18

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    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 4

    Problem Set Calculate the area of each triangle below. Figures are not drawn to scale.

    1.

    2.

    3.

    4.

    5. The Andersons were going on a long sailing trip during the summer. However, one of the sails on their sailboat ripped, and they have to replace it. The sail is pictured below.

    If the sailboat sales on are sail for $2 a square foot, how much will the new sale cost?

    10 in. 8 in. 17 in.

    15 in. 6 in.

    21 m

    72 m

    75 m

    21.9 km

    100.5 km

    75.8 km

    29.2 km

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  • Lesson 4: The Area of Obtuse Triangles Using Height and Base Date: 1/29/14

    S.19

    2014 Common Core, Inc. Some rights reserved. commoncore.org

    This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

    NYS COMMON CORE MATHEMATICS CURRICULUM 65 Lesson 4

    6. Darnell and Donovan are both trying to calculate the area of an obtuse triangle. Examine their calculations below.

    Darnells Work Donovans Work

    = 12 3 in. 4 in. = 6 in2

    = 12 12 in. 4 in. = 24 in2

    Which student calculated the area correctly? Explain why the other student is not correct.

    7. Russell calculated the area of the triangle below. His work is shown.

    = 12 43 cm 7 cm = 150.5 cm2

    Although Russell was told his work is correct, he had a hard time explaining why it is correct. Help Russell explain why is calculations are correct.

    8. The larger triangle below has a base of 10.14 m; the gray triangle has an area of 40.325 m2.

    a. Determine the area of the larger triangle if it has a height of 12.2 m. b. Let be the area of the unshaded (white) triangle in square meters. Write and solve an equation to determine

    the value of , using the areas of the larger triangle and the gray triangle.

    25 cm 7 cm

    24 cm 25 cm

    43 cm

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