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=20240727T001638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0727bb94bc6672e462ebdefbb6e114826f34db1f0b79830573c9ae867d024c90)
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=20240727T001638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=18fc6935eaad348bb12be58ed6f63fa558845fb0ec626e3b7d33c5d741eb7665)
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=20240727T001638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=af54f68e04240d625fd83404cb83f629b08d70ade4acd83f1a9fbd89d5c269d8)
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=20240727T001638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=85aa1fd4962c1743226147e8837682e77b9ffbd7d2b071ad6774a5ea76b94d50)
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=20240727T001638Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=52f9b50dd965b735831f02df9cda9e82d48fecc4eefe1862ec89253812392fd7)
Solution
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(From Unit 1, Lesson 3.)