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Lesson 14.1 Assignment

Name Date

Transforming to a New Level!Using Transformations to Determine Perimeter and Area

1. Franco translates rectangle JKLM so that it has one vertex on the origin. The result is rectangle J9K9L9M9. He claims that he doesn’t even have to use the Distance Formula to calculate the perimeter and area of this translated rectangle.

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6 J

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M9 L9

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4 8x

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a. Is Franco correct? Why or why not?

b. Maeko claims that you don’t have to use the Distance Formula or translate the rectangle in order to calculate the perimeter and area of the original rectangle. Is she correct? Why or why not?

c. Give an example of a case in which translating a rectangle to the origin would be extremely helpful in simplifying the calculations for determining the perimeter and area of the rectangle.

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2. Olivia translates rectangle WXYZ vertically up 1 unit and horizontally to the right 4 units to produce the image W9X9Y9Z9. Thom translates the rectangle vertically up 6 units and horizontally to the right 5 units to produce the image W0X0Y0Z0.

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W0

W9

Z0

Z9Z

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X0

X9

Y0

YY9

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4 6 8x

y

a. Would you prefer to use Olivia’s translation or Thom’s translation to determine the perimeter and area of the rectangle? Explain your reasoning.

b. Calculate the perimeter and area of the rectangle. Show your work.

Lesson 14.1 Assignment page 2

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Lesson 14.2 Assignment

Name Date

Looking at Something Familiar in a New WayArea and Perimeter of Triangles on the Coordinate Plane

1. Cisco claims that ____

GH is the height of triangle EFG, and Beth claims that ___

GJ is the height of triangle EFG.

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JH

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8x

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a. Who is correct? Support your answer with mathematics.

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b. Calculate the area of triangle EFG. Show your work.

2. A few years ago, Leon planted a small triangular garden in his backyard. Recently he has been thinking that the garden is too small. He now wants to double the area of the garden. His original garden is shown on the

coordinate plane. Each unit represents one square foot.

0 1 2 3 4

1

2

3

4

x

y

P

O

D

Lesson 14.2 Assignment page 2

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a. Describe two ways Leon could double the area of his garden.

b. Because of the location of Leon’s neighbors, he cannot extend the garden any further horizontally. Use this information to manipulate the image POD representing Leon’s garden to double the area. Label the image as PO9D.

c. Determine the area of the original garden and the new garden to verify that the area has doubled.

Lesson 14.2 Assignment page 3

Name Date

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One Figure, Many NamesArea and Perimeter of Parallelograms on the Coordinate Plane

1. Joel knows that rectangles and parallelograms are closely related and the formulas to determine the area of both figures are the same. He multiplies the lengths of

____ WX and

____ WZ to determine the area of

parallelogram WXYZ.

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YZ

W

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a. Has Joel correctly determined the area of the parallelogram? Explain your reasoning.

b. Calculate the area of parallelogram WXYZ. Show your work.

Lesson 14.3 Assignment

Name Date

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Lesson 14.3 Assignment page 2

2. Parallelograms JKLM and JKPR are given. Without calculating the areas, determine whether or not the area of parallelogram JKPR is twice that of the area of parallelogram JKLM. Explain how you determined your answer.

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Lesson 14.4 Assignment

Name Date

Let’s Go Halfsies!Determining the Perimeter and Area of Trapezoids and Composite Figures

1. Trapezoid QRST is given.

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a. Determine the perimeter of trapezoid QRST. Show your work. Round your answer to the nearest hundredth.

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Lesson 14.4 Assignment page 2

b. Determine the area of trapezoid QRST. Show your work and explain how you determined your answer.

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Lesson 14.4 Assignment page 3

Name Date

2. Composite figure ABCDEFG is given.

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D

E

G F

A B

C

a. Determine the perimeter of figure ABCDEFG.

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Lesson 14.4 Assignment page 4

b. Determine the area of figure ABCDEFG.

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