Lesson 6
Area of Parallelograms
Let's practice finding the area of parallelograms.
Problem 1
Which three of these parallelograms have the same area as each other?
![Four parallelograms, labeled A, B, C, and D.](https://cms-im.s3.amazonaws.com/KDP5kft6Bn3jGd78FknaHnFP?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP.New.Image.12.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP.New.Image.12.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234834Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d0ddd3d342f389b04012c045382c2ff49c63153b554a4576ebd538b73f5828a3)
A
B
C
D
Problem 2
Which pair of base and height produces the greatest area? All measurements are in centimeters.
\(b = 4\), \(h=3.5\)
\(b = 0.8\), \(h=20\)
\(b = 6\), \(h=2.25\)
\(b = 10\), \(h=1.4\)
Problem 3
Here are the areas of three parallelograms. Use them to find the missing length (labeled with a "?") on each parallelogram.
A: 10 square units
B: 21 square units
C: 25 square units
![Three parallelograms labeled A, B, C.](https://cms-im.s3.amazonaws.com/xzBKx2vm94wTD8JdQt1uG46d?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP_Image_9.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP_Image_9.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234834Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cba231547b3212a2839231c83e588d26f4c6de54e828a2756145f34f954afb28)
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234834Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=567bc76342af97542edcbdc6de6653068157481e202b09c17d0552ac2ea9cad1)
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?
Problem 5
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234834Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e52971e9caef0b363587265aa847683425a23112d356a9a157262b7fa8f96367)
e
f
g
h
j
k
n
Problem 6
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234834Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=178b5c801a2c9ae638e4f637271eb157baf45fdd78b09cba192e3db30a074ffc)