1. Class Greeting

2. Areas of Composite Figures and Irregular Shapes
Chapter 9 – Lesson 3
Areas of Composite Figures and Irregular Shapes

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

4. Vocabulary
composite figure

5. 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.

6. How could we calculate the area of an irregular figure?

7. Example 1: Finding the Areas of Composite Figures by Adding
Find the shaded area.
Round to the nearest tenth.
Area of the trapezoid:
Area of the semicircle:
Shaded area:
 ≈ mm2

8. Check It Out! Example 1a
Find the shaded area.
Area of the parallelogram:
A = bh = 8(5) = 40 ft2
Area of the triangle:
Shaded area:
= 65 ft2

9. Check It Out! Example 1b
Find the shaded area.
Round to the nearest tenth.
Area of the triangle:
Area of the semicircle:
234 –  ≈ ft2
Shaded area:

10. Check It Out! Example 1c
Find the shaded area.
Round to the nearest tenth.
Area of the circle:
Area of the trapezoid:
Shaded area:
100 – 128 ≈ cm2

11. Example 2
A company receives an order for 65 pieces of fabric in the given shape. Each piece is to be dyed red. To dye 6 in2 of fabric, 2 oz. of dye is needed.
How much dye is needed for the entire order?
Area of the circle:
Area of the square:
Shaded area:
2.25 + 9 ≈ 16.1 in2
Area of the 65 pieces:
65(16.1) ≈ in2
scale factor: 3 to 1

12. Example 3
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.
Area of rectangle:
A = lw = (3)(2) = 6 ft2
Area of half circle:
Area of isosceles triangle:
Area of right triangle:
The shaded area is about 12 ft2.

13. Check It Out! Example 3
Use a composite figure to estimate the shaded area. The grid has squares with side lengths of 1 ft.
Area of the square:
Area of triangle:
3 triangles:
3 ft2
Area of the trapezoid:
The shaded area is about 9 ft2.

14. Lesson Summary: Objectives
Use the Area Addition Postulate to find the areas of composite figures.
Use composite figures to estimate the areas of irregular shapes.

15. Preview of the Next Lesson:
Objectives
Find the perimeters and areas of figures in a coordinate plane.

16. Kahoot!

17. Stand Up Please