A composite figure is a geometric shape made up of more than one polygon or plane figure. Typically, any line segments shared by the polygons in a composite figure are not drawn. In figure ABCDE below, is shared by rectangle ABCF and triangle FDE and therefore is not drawn. Students should have opportunities to compose and decompose geometric figures by manipulating polygons (rectangles and triangles). The more that students work on seeing the individual polygons that make up composite figures, the better they will understand how to determine their areas.

This figure is a rectangle and a triangle combined together. So the area is:

A	= lw + bh = (10)(5) + (6) = 50 + 18 = 68

The area of the figure is 68 square feet.

One way to help students see the pieces that make up composite figures is a great puzzle called tangrams. The puzzle consists of seven tangram pieces — a square, 5 triangles, and a parallelogram. The tangram is shown below. One goal of the puzzle is to recreate composite figures like everyday common objects and animals using all seven pieces. This teaches students to look for polygons in a composite figure. Once they see how the pieces are related by shape and size, finding the area of a composite figure will be simpler for them.

When you look at the tangram, these are the different pieces that make up the puzzle.

In each puzzle there are two parts 1 and 2 and one each of parts 3, 4, and 5.

• Suppose we let part 2 have an area of 1 sq. unit. Determine the area of each of the other pieces.

  Answer: Part 1 has an area of 4 sq. units, part 3 has an area of 2 sq. units, part 4 has an area of 2 sq. units and part 5 has an area of 2 sq. units.

• If part 2 has an area of 4 sq. units, what is the area of the original puzzle with all seven pieces?

  Answer: 16 sq. units

Suggested resource: The Fun with Tangrams Kit, Susan Johnston, Dover Publications.