Lesson 5
Areas of Parallelograms
Problem 1
Select all segments that could represent a corresponding height if the side \(m\) is the base.
![A parallelogram with a bottom side labeled m and a right side labeled n. Dashed lines e, f, j, and k are drawn perpendicular to side m, and dashed lines g and h are drawn perpendicular to side n.](https://cms-im.s3.amazonaws.com/tFqfcBp8q4QSRV2SEENK4hVi?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP.New.Image.10.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP.New.Image.10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T121041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1a125e336fa5a70a065fc5f6601b66852b31ebebd8fb430b1c02c7c5b752106d)
e
f
g
h
j
k
n
Solution
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Problem 2
Find the area of each parallelogram.
![3 parallelograms on a grid, labeled A, B, C.](https://cms-im.s3.amazonaws.com/foFfv3JuZoW1XShCTGovW3ch?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP_Image_7.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP_Image_7.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T121041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f05a6e9ecf32d9e59e5c1688a64fed40c4c2e8ead6bb6112e5f1bac14a564d6a)
Solution
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Problem 3
Find the area of each parallelogram.
![3 parallelograms labeled A, B, C.](https://cms-im.s3.amazonaws.com/tWaYddDfgxHuVywo2yGisFdo?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP_Image_8.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP_Image_8.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T121041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=25e5ab530775d418558dd95b024008527459ec5418736ab772aca7fedfd68633)
Solution
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Problem 4
The Dockland Building in Hamburg, Germany is shaped like a parallelogram.
![A photograph of the Dockland Building in Hamburg, Germany. The building is shaped like a parallelogram.](https://cms-im.s3.amazonaws.com/kYiQYtUeQZvPnawBV2c1BoD5?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP_Image_10.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP_Image_10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T121041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e902f94c328b1d3047ac5ec0ecfe2be58d7e1f44f4718cc478c1ddfee5740098)
If the length of the building is 86 meters and its height is 55 meters, what is the area of this face of the building?
Solution
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Problem 5
Do you agree with each of these statements? Explain your reasoning.
- A parallelogram has six sides.
- Opposite sides of a parallelogram are parallel.
- A parallelogram can have one pair or two pairs of parallel sides.
- All sides of a parallelogram have the same length.
- All angles of a parallelogram have the same measure.
Solution
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(From Unit 1, Lesson 4.)Problem 6
A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.
- What is the area, in square meters, of 6 triangles? If you get stuck, consider drawing a diagram.
- How many triangles are needed to compose a region that is \(1\frac 12\) square meters?
Solution
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(From Unit 1, Lesson 2.)Problem 7
Find the area of the shaded region. All measurements are in centimeters. Show your reasoning.
![A shaded rectangle located at an angle within a larger rectangle.](https://cms-im.s3.amazonaws.com/FHSqJnwV7jNK71sC9vXjDo9b?response-content-disposition=inline%3B%20filename%3D%226-6.1.A.PP.New.Image.18b.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.A.PP.New.Image.18b.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T121041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1f16eb53e38050ef60f180a16182f259aa6b303c20d4a9d5f437c2953b5b5684)
Solution
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(From Unit 1, Lesson 3.)