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=20240726T234649Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ea3f22c5796b273aafe5d84a757457d91589f81093d491045d9c048f01a4431c)
Solution
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Problem 2
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Decompose and rearrange this parallelogram to make a rectangle.
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What is the area of the parallelogram? Explain your reasoning.
Solution
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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=20240726T234649Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3a0b1939649abdfb294df3ce41800652cb1a6bb99f06945ad5b5c3da7bd22a3e)
Solution
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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=20240726T234649Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=bd52d16072850c80ebdaf5ab14dbb889b26b5ef715f48bf5a4ef44b6aaeb3f89)
Solution
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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=20240726T234649Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b72bba41c084294819683afefa739233f2be08f7d95a9b1738053ff3b065585a)
![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=20240726T234649Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b895867c3c189fdca2d9bedd38ce974b04663d11102984e0ab1df6b81edbcdfc)
Solution
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(From Unit 1, Lesson 3.)Problem 6
Find the area of the rectangle with each set of side lengths.
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5 in and \(\frac13\) in
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5 in and \(\frac 43\) in
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\(\frac 52\) in and \(\frac 43\) in
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\(\frac 7 6\) in and \(\frac 67\) in
Solution
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(From Unit 1, Lesson 1.)