Lesson 4

Parallelograms

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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.

 

Solution

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Problem 2

  1. Decompose and rearrange this parallelogram to make a rectangle.

    parallelogram on a grid. base = 9 units, height = 5 units. 

  2. 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

 

Solution

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Problem 4

Explain why this quadrilateral is not a parallelogram.

A quadrilateral on a grid.

 

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.
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.

 

Solution

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(From Unit 1, Lesson 3.)

Problem 6

Find the area of the rectangle with each set of side lengths.

  1. 5 in and \(\frac13\) in

  2. 5 in and \(\frac 43\) in

  3. \(\frac 52\) in and \(\frac 43\) in

  4. \(\frac 7 6\) in and \(\frac 67\) in

Solution

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(From Unit 1, Lesson 1.)