Lesson 5
Bases and Heights of Parallelograms
Let’s investigate the area of parallelograms some more.
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=20240727T005359Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6430183fe0b825b178e338935f7725fedf7d8bfccda9efa5daadecfbac250d05)
A:
A
B:
B
C:
C
D:
D
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=20240727T005359Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=be2d639c16923d0ef35ddeb93a8499f3a0f99c01ec01874a92e22614e81d3613)
Draw a segment showing the height corresponding to that base.
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=20240727T005359Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6ca0406a2dad253d7ad9f59d8f0c47861793bd815a06efa1d17fc4d0c6598771)
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=20240727T005359Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=de86d652804573e101a862a8775d255909711360e6ef60fa85dda9e0afcf8d56)
A:
6 units
B:
4.8 units
C:
4 units
D:
5 units
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=20240727T005359Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1ed4b00ae50ac87ec4dd6b96d44a2c9b106546973fc03157895b7a2a211dfd2c)
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.
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?