Area of a Complex Figure: Trapezoid

Contributor: Erika Wargo. Lesson ID: 12585

A trapezoid is not something a circus performer swings on; it is a complex figure that can be broken up into other figures in order to find its area. Learn the simple tricks for finding complex areas!


Middle School

learning style
personality style
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!


You are responsible for painting the walls of your new treehouse. How will you know how much paint to buy? How do you find the total area that you will paint?

Complex figures are made up of more than one shape.

Sometimes, complex figures are called irregular shapes because they are a combination of regular shapes. Irregular shapes do not have all equal sides or equal angles. There is not one formula you can use to find area, and you have to break the irregular shape into regular shapes that you know the area formula for, such as circles, squares, rectangles, and triangles.

Before you learn how to decompose, or break apart, a complex figure, review the area formulas for regular shapes:

shape area formula


side x side


length x width


1/2 (base)(height)


Now that you are familiar with the area formulas for regular shapes, learn about how to find the area of a complex or irregular figure by completing the following steps:

  1. Go to Area of Irregular Figures (Scholastic Inc. Study Jams!) and click on the green button labeled STEP BY STEP to watch how to divide an irregular figure into regular, smaller shapes. Note: In the video, they mention that the area of a rectangle is “base x height,” which is another way to say “length x width." Click on the NEXT and SHOW ME buttons to progress through the steps.
  2. Click on WACTH OUT! to learn more about breaking down a complex figure with a triangle and finding the missing side measurements of a shape.

In your math journal, write a response to the following:

  1. In your own words, explain the steps used to find the area of a complex or irregular figure.
  2. Is there more than one way to break down a complex shape? Explain with examples.

A trapezoid can be considered a complex shape. Draw lines on the trapezoid to decompose it into familiar shapes:

What familiar shapes do you see in the trapezoid?

The method of breaking down a complex figure works when you are given enough information about the lengths of the sides. There is a faster and more efficient way of calculating the area of a trapezoid using a specific formula.

As you watch the video by Math Meeting, Area of a trapezoid, to learn about the formula used to find the area of a trapezoid, respond to the following in your math journal:

  1. What is the formula for a trapezoid?
  2. What does each part of the formula represent? A = _______ b1 = _______ b2 = _______ h = _______
  3. Why might it be helpful to label the parts of the trapezoid according to the formula parts?


In your math journal, write a response to the question:

Would you rather decompose a complex figure and find the area of smaller shapes or use one formula to find the area of the entire shape? Explain.

In the Got It? section, you will practice calculating the area of complex figures in interactive games and practice.

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