9-6 Area of Irregular Figures

Course 2

Math MinuteMath Minute

Lesson PresentationLesson Presentation

VocabularyVocabulary

Math Minute

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. yd

31 m2

540 in2

Course 2

9-6 Area of Irregular Figures

4 yd2

Learn to find the area of irregular figures.

Course 2

9-6 Area of Irregular Figures

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.

Course 2

9-6 Area of Irregular Figures

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

Course 2

9-6 Area of Irregular Figures

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 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

Course 2

9-6 Area of Irregular Figures

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

Area of the rectangle:

8 yd

9 yd

Continued

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

Substitute 2 for b and 9 for h.

Course 2

9-6 Area of Irregular Figures

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

Now You Try…

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

Course 2

9-6 Area of Irregular Figures

9 m

16 m

Step 2: Find the area of each smaller figure.

Area of the parallelogram:

Continued

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

Substitute 3.14 for and 8 for r.

16 m

Course 2

9-6 Area of Irregular Figures

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

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

Course 2

9-6 Area of Irregular Figures

9 m

16 m

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.

Course 2

9-6 Area of Irregular Figures

Example 3: Finding the Shaded Region

Find the area of the shaded region Use 3.14 for pi.

Course 2

9-6 Area of Irregular Figures

2 cm

4 cm

4 cm

Step 1: Write the formula.

Step 2: Substitute values.

A = area of square – area of circleA = (l x w) – ( πr2)

A = (4 x 4) – (3.14 x 22)

A = (16) – (3.14 x 4)Step 3: Solve.

A = (16) – (12.56)

A = 3.44 cm2