Lesson 4
Parallelograms
Let’s investigate the features and area of 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=20240726T234707Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f7509b2e5d486144880aafbf65fe033174b744878670c725c2d45df4ae607f73)
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.
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=20240726T234707Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=03d6ee6ecaf2231c90b36e15a7973fe7e84274c605e9d3cfff19870d4b9ce91e)
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=20240726T234707Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d6cb13cba8356249e45d8444e0a92bb064abc7d8174faa0e02205a31cb222fbc)
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=20240726T234707Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a8adc51ccb3910d1e3c35985a7420bac4236015656451bc8b5f9e3b161fc69d0)
![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=20240726T234707Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=77d7c322324a9cb84bff810db228096398dd60c3468be97ffab17139ee3704c7)
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