1. Objectives
Use the Area Addition Postulate to find the areas of composite figures.
Use composite figures to estimate the areas of irregular shapes.

2. A composite figure is made up of simple
shapes, such as triangles, rectangles,
trapezoids, and circles. To find the area of a composite figure, find the areas of the simple shapes and then use the Area Addition Postulate.

3. Example 1A: Finding the Areas of Composite Figures by Adding
Find the shaded area. Round to the nearest tenth, if necessary.
Divide the figure into parts.
area of half circle:

4. Example 1A Continued
area of triangle:
area of the rectangle:
A = bh = 20(14) = 280 mm2
shaded area:
50 ≈ mm2

5. Example 2: Finding the Areas of Composite Figures by Subtracting
Find the shaded area. Round to the nearest tenth, if necessary.
area of a triangle:
area of the half circle:
Subtract the area of the half circle from the area of the triangle.
area of figure:
234 –  ≈ ft2

6. Example 2: Finding the Areas of Composite Figures by Subtracting
Find the shaded area. Round to the nearest tenth, if necessary.
area of circle:
A = r2 = (10)2 = 100 cm2
area of trapezoid:
area of figure:
100 –128  cm2

7. To estimate the area of an irregular shape, you can sometimes use a composite figure.
First, draw a composite figure that resembles the irregular shape.
Then divide the composite figure into simple shapes.

8. Check It Out! Example 4
Use a composite figure to estimate the shaded area. The grid has squares with side lengths of 1 ft.
Draw a composite figure that approximates the irregular shape. Find the area of each part of the composite figure.

9. Check It Out! Example 4 Continued
area of triangle:
area of half circle:
area of rectangle:
A = lw = (3)(2) = 6 ft2
The shaded area is about 12 ft2.