Lesson 4
Parallelograms
Problem 1
Select all of the parallelograms. For each figure that is not selected, explain how you know it is not a parallelogram.
![5 figures labeled A, B, C, D, E.](https://cms-im.s3.amazonaws.com/ESgSiRbMtJpvQv3vtmRou97b?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP_Image_1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP_Image_1.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=20240726T235414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6dda8e14e6202a55c2b1d7b3e6d6e402fcd7a5386f227d1e55ba7b23dbfe3eee)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 2
-
Decompose and rearrange this parallelogram to make a rectangle.
-
What is the area of the parallelogram? Explain your reasoning.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 3
Find the area of the parallelogram.
![A parallelogram with one side labeled 3.2 centimeters, and another side labeled 10 centimeters. A dashed line perpendicular to the 10 centimeter sides is labeled 3 centimeters](https://cms-im.s3.amazonaws.com/aqSHoFW7BkZEMSarTHTKiiKB?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP.New.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP.New.Image.05.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=20240726T235414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a541f225156fdaa801445ba79506691b7a1a1c8a79fdf7d0c6f5cd23bbac43f6)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 4
Explain why this quadrilateral is not a parallelogram.
![A quadrilateral on a grid.](https://cms-im.s3.amazonaws.com/tyb9vPgCcgiJkUr21CeZ6xsR?response-content-disposition=inline%3B%20filename%3D%226-6.1.C.PP.New.Image.01a.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.C.PP.New.Image.01a.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=20240726T235414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=90fe47b3816de8540d75aab217921e67c6a3a91e89e862711bb62be7802eddde)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 5
Find the area of each shape. Show your reasoning.
![A shape with eight sides drawn on a grid.](https://cms-im.s3.amazonaws.com/iSegiss6sqSUhL9iwodj6cf5?response-content-disposition=inline%3B%20filename%3D%226-6.1.A.PP.New.Image.17a.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.A.PP.New.Image.17a.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=20240726T235414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fc8fd1769c4d7af915fa9d00b7bb53a236f30abf9618d8e0aaaadbc066ea49be)
![A shape with six sides. It is 9 units long and six units wide at it’s widest point. Two vertical sides connect four sloped sides, which meet at either end of the shape.](https://cms-im.s3.amazonaws.com/jyv4SaXG4RF7LqSgW7uSj8Vo?response-content-disposition=inline%3B%20filename%3D%226-6.1.A.PP.New.Image.17b.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.A.PP.New.Image.17b.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=20240726T235414Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=58b889d1f0d9197fd0437e2ba92d47d0c33b2e0cad21d2d9317c791f347b166c)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 3.)Problem 6
Find the area of the rectangle with each set of side lengths.
-
5 in and \(\frac13\) in
-
5 in and \(\frac 43\) in
-
\(\frac 52\) in and \(\frac 43\) in
-
\(\frac 7 6\) in and \(\frac 67\) in
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 1.)