Warm Up Find the area of the following figures.

9-6 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


Problem of the Day

It takes a driver about second to begin breaking after seeing something in the road. How many feet does a car travel in that time if it is going 10 mph? 20 mph? 30 mph? 11 ft; 22 ft; 33 ft

3 4


Vocabulary

composite figure

Learn to find the 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.


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.


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


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:


Additional Example 2 Continued


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




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




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


Check It Out: Example 2 Continued


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




A = 72 + 9 = 81

The area of the figure is about 81 yd2.

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


Additional Example 3: Problem Solving Application

The Wrights want to tile their entry with one-square-foot tiles. How much tile will they need?

5 ft

8 ft

4 ft

7 ft

t



11 Understand the Problem

Rewrite the question as a statement.• Find the amount of tile needed to cover the

entry floor.

List the important information:• The floor of the entry is an irregular shape.• The amount of tile needed is equal to the

area of the floor.



Find the area of the floor by separating the figure into familiar figures: a rectangle and a trapezoid. Then add the areas of the rectangle and trapezoid to find the total area.

22 Make a Plan

5 ft

8 ft

4 ft

7 ft

t



Solve33Find the area of each smaller figure.

A = lw

A = 8 • 5

A = 40


Area of the trapezoid:

A = 24

A = h(b1 + b2)12

__

A = • 4(5 + 7)12__

A = • 4 (12)12__

Add the areas to find the total area.

A = 40 + 24 = 64

The Wrights’ need 64 ft2 of tile.



Look Back44

The area of the entry must be greater than the area of the rectangle (40 ft2), so the answer is reasonable.



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

6 ft

23 ft

18 ft5 ft



11 Understand the Problem

Rewrite the question as a statement.• Find the amount of wallpaper needed to

cover the loft wall.

List the important information:• The wall of the loft is an irregular shape.• The amount of wallpaper needed is equal to

the area of the wall.



Find the area of the wall by separating the figure into familiar figures: a rectangle and a triangle. Then add the areas of the rectangle and triangle to find the total area.

22 Make a Plan

6 ft

23 ft

18 ft5 ft



Solve33Find the area of each smaller figure.

A = lw

A = 18 • 6

A = 108


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__



Look Back44

The area of the wall must be greater than the area of the rectangle (108 ft2), so the answer is reasonable.


1. Identify the perimeter and area of the figure.

A. 50 cm; 42 cm2

B. 50 cm; 54 cm2

C. 34 cm; 54 cm2

D. 34 cm; 42 cm2

Lesson Quiz for Student Response Systems


2. Identify the perimeter and area of the figure.

A. 14.85 in.; 31.63 in2

B. 22.7 in.; 31.63 in2

C. 14.85 in.; 15.81 in2

D. 22.7 in.; 15.81 in2

Lesson Quiz for Student Response Systems

Warm Up Find the area of the following figures.

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