Composite Figures Are Fun!

Composite figures are a wonderful opportunity to have fun with art in math and cover Common Core standards at the same time. To find the area of composite figures, students must “decompose” them into simple geometric shapes, find the area of each of those, and combine them to find the total area.

The problem is that some children lack the perspective to visualize these other shapes. The best way to help them, in my experience, is through art projects and activities.


A tangram is a set of seven geometric shapes (called “tans”) which fit together to form different shapes. Given an outline, students must arrange the tans so that they will fit the puzzle.

Tangrams and puzzles can be printed out free at several online sites, including Activity Village.

Working with the puzzles helps children develop the perspective they need to decompose composite figures, and children really enjoy “playing” with them.

After they have some experience with traditional tangram puzzles, I have students use the tans to create their own animals for our Tangram Zoo, figuring the area of each animal.

The lab sheet for this activity may be downloaded free here.

Mountain Village

Teacher Led Center

Materials: rulers, construction paper, scissors, pencils

Instructions for students:

        1. On a piece of construction paper, draw a square having an area of 9 sq. in.  – Lead students to an understanding that sides must be 3 inches long in order for the area to be 9 sq. in.          

        2. Adjacent to one side, construct a triangle with a height of 2 inches. – My children inevitably tried to use the length of one of the sides of the triangle as its height. Since this was in my center, I was able to clarify this.

        3.  Find the area of the triangle. – The base is 3 inches so B X H = 6. Because it is a triangle, this must be divided by 2 making the area 3 sq. in.

        4.  Find the total area of the house. (12 sq. in.)

        5.  Cut out your house, turn it over, and exchange with someone else.

        6.  Decompose the house into a square and a triangle.

        7.  Write the area in the center of each figure. – As they completed this step, I had them explain to me how they arrived at their answers.

Go to Teaching Math With Art from Composite Figures

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