9-3 Area of Irregular Figures

Warm Up

Find the area of the following figures.

1. A triangle with a base of 12.4 m and a height of 5 m

2. A parallelogram with a base of 36 in. and a height of 15 in.

3. A square with side lengths of 2.05 yd

31 m2

540 in2

4.2025 yd2

9-3 Area of Irregular Figures

Learn to find the area of irregular figures.

9-3 Area of Irregular Figures

Vocabulary

composite figure

9-3 Area of Irregular Figures

A composite figure is made up of simple geometric shapes, such as triangles and rectangles. You can find the area of an irregular figure by separating it into non-overlapping familiar figures. The sum of the areas of these figures is the area of the irregular figure. You can also estimate the area of an irregular figure by using graph paper.

9-3 Area of Irregular Figures

Additional Example 1: Estimating the Area of an Irregular Figure

Estimate the area of the figure. Each square represents one square yard.

Count the number of filled or almost-filled squares: 45 squares.

Count the number of squares that are about half-full: 10 squares.

Add the number of filled squares plus ½ the number of half-filled

squares: 45 + ( • 10) = 45 + 5 =501 2

The area of the figure is about 50 yd2.

9-3 Area of Irregular Figures

Check It Out: Example 1

Estimate the area of the figure. Each square represents one square yard.

Count the number of filled or almost-filled squares: 11 red squares.Count the number of squares that are about half-full: 8 green squares.Add the number of filled squares plus ½ the number of half-filled

squares: 11 + ( • 8) = 11 + 4 =15.1 2

The area of the figure is about 15 yd .2

9-3 Area of Irregular Figures

Additional Example 2: Finding the Area of an Irregular Figure

Find the area of the irregular figure. Use 3.14 for .

Use the formula for the area of a parallelogram.Substitute 16 for b.Substitute 9 for h.

A = bh

A = 16 • 9

A = 144

Step 1: Separate the figure into smaller, familiar figures.

16 m

9 m

16 m

Step 2: Find the area of each smaller figure.

Area of the parallelogram:

9-3 Area of Irregular Figures

Additional Example 2 Continued

Find the area of the irregular figure. Use 3.14 for .

Substitute 3.14 for and 8 for r.

16 m

9 m

16 m

Area of the semicircle:

A = (r)12__

The area of a semicircle

is the area of a circle.12

A ≈ (3.14 • 82)12

__

A ≈ (200.96) 12

__

Multiply.A ≈ 100.48

9-3 Area of Irregular Figures

Additional Example 2 Continued

Find the area of the irregular figure. Use 3.14 for .

A ≈ 144 + 100.48 = 244.48

The area of the figure is about 244.48 m2.

Step 3: Add the area to find the total area.

16 m

9 m

16 m

9-3 Area of Irregular Figures

Check It Out: Example 2

Find the area of the irregular figure. Use 3.14 for .

Use the formula for the area of a rectangle.Substitute 8 for l.Substitute 9 for w.

A = lw

A = 8 • 9

A = 72

Step 1: Separate the figure into smaller, familiar figures.

3 yd

9 yd Step 2: Find the area of each smaller figure.

Area of the rectangle:

8 yd

9 yd

9-3 Area of Irregular Figures

Check It Out: Example 2 Continued

Find the area of the irregular figure. Use 3.14 for .

Substitute 2 for b and 9 for h.

Area of the triangle:

A = bh12__

The area of a triangle

is the b • h.12

A = (2 • 9)12

__

A = (18) 12

__

Multiply.A = 9

2 yd

9 yd

8 yd

9 yd

9-3 Area of Irregular Figures

Check It Out: Example 2 Continued

Find the area of the irregular figure. Use 3.14 for .

A = 72 + 9 = 81

The area of the figure is about 81 yd2.

Step 3: Add the area to find the total area.

9-3 Area of Irregular Figures

Check It Out: Example 3

The Franklins want to wallpaper the wall of their daughters loft. How much wallpaper will they need?

6 ft

23 ft

18 ft5 ft

9-3 Area of Irregular Figures

Check It Out: Example 3 Continued

Solve33Find the area of each smaller figure.

A = lw

A = 18 • 6

A = 108

Area of the rectangle:

Area of the triangle:

Add the areas to find the total area.

A = 108 + 27.5 = 135.5

The Franklins need 135.5 ft2 of wallpaper.

A = 27.5

A = bh12__

A = (5 • 11)12__

A = (55)12__

9-3 Area of Irregular Figures

Lesson QuizFind the perimeter and area of each figure.

1.

2.

31.42 cm, 62.13 cm2

39.1 ft, 84 ft2