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.

 

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.

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

 

Problem 4

Explain why this quadrilateral is not a parallelogram.

A quadrilateral on a grid.

 

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.

 

(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

(From Unit 1, Lesson 1.)