Lesson 6
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T002102Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5a2f945880c72628aca70a86397d657919c8ad3b03fceaac37512a70245a1b34)
A
B
C
D
Solution
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Problem 2
Which pair of base and height produces the greatest area? All measurements are in centimeters.
\(b = 4\), \(h=3.5\)
\(b = 0.8\), \(h=20\)
\(b = 6\), \(h=2.25\)
\(b = 10\), \(h=1.4\)
Solution
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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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T002102Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e745765cdbc8a4f4157a8b0afa823e83ad05bb71943cc2d6c9903d91366f6e0b)
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=20240727T002102Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=964e6aa92a9619f23ca583d910f643ac8cf2aac7ad7faef3139086f245be98aa)
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
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=20240727T002102Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8c7e3d7be0f204ef05041047905999709af9d3b792888e7a30442e192e1bed3d)
e
f
g
h
j
k
n
Solution
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(From Unit 1, Lesson 5.)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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T002102Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=53fe2153697979cce80b54a5b8b8d851b3a9418f9d20a1bb1cbcd3e938c3a663)
Solution
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(From Unit 1, Lesson 3.)