Lesson 5
Bases and Heights of Parallelograms
Problem 1
Select all parallelograms that have a correct height labeled for the given base.
![4 parallelograms on a grid, labeled A, B, C, D.](https://cms-im.s3.amazonaws.com/gBbqFY5m9X7vukA14D4NaRaY?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP_Image_6.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP_Image_6.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=20240727T034322Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a3a3dd24ec62416635347b6d520116311fee021be9d1f78970df2927460f2745)
A
B
C
D
Solution
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Problem 2
The side labeled \(b\) has been chosen as the base for this parallelogram.
![parallelogram on a grid. base = 4 units, distance from bottom side to top side = 2 units. Left and right sides are slanted.](https://cms-im.s3.amazonaws.com/k3qkKdiF6WMWj9qQhkK9BGRe?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP_Image_11.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP_Image_11.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=20240727T034322Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=06c41239afd3f2ad3008653e1ff8fd938c2d6b8bda197746d55720993dc33daa)
Draw a segment showing the height corresponding to that base.
Solution
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Problem 3
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=20240727T034322Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=edda9bdae730d309333ac1fd1ed37adf78c521293582e55c7274da342efe29ec)
Solution
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Problem 4
If the side that is 6 units long is the base of this parallelogram, what is its corresponding height?
![Parallelogram.](https://cms-im.s3.amazonaws.com/ZVeRetUqnXsD2oSscb6icyVH?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP.New.Image.08.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP.New.Image.08.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=20240727T034322Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c72b3d3f0d24909d54a2d458d7956c8efa9a960234bf8ecfb8f59c09edeefdda)
6 units
4.8 units
4 units
5 units
Solution
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Problem 5
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=20240727T034322Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5e66e5b8d4a35be49bc346622cab63fd7914a23d34a811dcff2b46b75bd26e1e)
Solution
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Problem 6
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 7
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.)