Lesson 6Area of Parallelograms

Learning Goal

Let’s practice finding the area of parallelograms.

Learning Targets

  • I can use the area formula to find the area of any parallelogram.

Lesson Terms

  • base (of a parallelogram or triangle)
  • height (of a parallelogram or triangle)
  • parallelogram

Warm Up: Missing Dots

Problem 1

An arrangement of dots.

How many dots are in the image?

How do you see them?

Activity 1: More Areas of Parallelograms

Problem 1

open applet in presentation mode

  1. Calculate the area of the given figure in the applet. Then, check if your area calculation is correct by clicking the Show Area checkbox.

  2. Uncheck the Area checkbox. Move one of the vertices of the parallelogram to create a new parallelogram. When you get a parallelogram that you like, sketch it and calculate the area. Then, check if your calculation is correct by using the Show Area button again.

  3. Repeat this process two more times. Draw and label each parallelogram with its measurements and the area you calculated.

  1. Calculate the area of the given figure in the applet. Then, check if your area calculation is correct by clicking the Show Area checkbox.

  2. Uncheck the Area checkbox. Move one of the vertices of the parallelogram to create a new parallelogram. When you get a parallelogram that you like, sketch it and calculate the area. Then, check if your calculation is correct by using the Show Area button again.

  3. Repeat this process. Draw and label the parallelogram with its measurements and the area you calculated.

  4. Repeat this process one last time. Draw and label the parallelogram with its measurements and the area you calculated.

Print Version

Find the area of each parallelogram. Show your reasoning.

  1. parallelogram with base measure 10 cm and height measure 6 cm.
  2. parallelogram with measurements in cm.
  3. parallelogram with measurements in cm.
  4. parallelogram

Problem 2

In Parallelogram b of the first problem, what is the corresponding height for the base that is 10 cm long? Explain or show your reasoning.

Problem 3

  1. Explain why their areas are equal.

  2. Drag points to create two new parallelograms that are not identical copies of each other but that have the same area as each other. Sketch your parallelograms and explain or show how you know their areas are equal. Then, click on the Check button to see if the two areas are indeed equal.

open applet in presentation mode
Print Version

Two different parallelograms and both have an area of 20 square units. Neither parallelogram is a rectangle.

On the grid, draw two parallelograms that could be and .

A blank grid

Are you ready for more?

Problem 1

Here is a parallelogram composed of smaller parallelograms. The shaded region is composed of four identical parallelograms. All lengths are in inches.

A green parallelogram composed of smaller parallelograms with a white parallelogram in the middle.

What is the area of the unshaded parallelogram in the middle? Explain or show your reasoning.

Lesson Summary

Any corresponding pair of base and height can help us find the area of a parallelogram, but some base-height pairs are more easily identified than others.

  • When a parallelogram is drawn on a grid and has horizontal sides, we can use a horizontal side as the base. When it has vertical sides, we can use a vertical side as the base. The grid can help us find (or estimate) the lengths of the base and of the corresponding height

Two parallelograms drawn on two grids. The first parallelogram has horizontal sides that are each 8 units long with angled sides that rise 2 vertical units over 4 horizontal units. The bottom horizontal side of the shape is labeled “b”. A 2-unit perpendicular segment labeled “h” connects the horizontal sides. The second parallelogram has two vertical sides that are each 6 units long, with angles sides that rise 4 vertical units over 4 horizontal units. The left vertical side is labeled “b”. A 4-unit perpendicular segment labeled “h” connects one vertex of the vertical side to a point on the other vertical side.

  • When a parallelogram is not drawn on a grid, we can still find its area if a base and a corresponding height are known.

A parallelogram with side lengths 10 units and 8 units. An 8-unit perpendicular segment connects one vertex of the 8 unit side to a point on the other 8 unit side.

In this parallelogram, the corresponding height for the side that is 10 units long is not given, but the height for the side that is 8 units long is given. This base-height pair can help us find the area.

Regardless of their shape, parallelograms that have the same base and the same height will have the same area; the product of the base and height will be equal. Here are some parallelograms with the same pair of base-height measurements.

Four different parallelograms. Each parallelogram has a base labeled 3 and a height labeled 4.