1. Learn to find the area of irregular figures.

2. 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.

3. Example 1
Estimate the area of the figure. Each square represents one square yard.
Count the number of filled or almost-filled squares: 46 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: 46 + ( • 10) = =51
1 2
The area of the figure is about 51 yd2.

4. Count the number of filled or almost-filled squares: 11 red squares.
Example 2
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) = =15.
1 2
The area of the figure is about 15 yd . 2

5. Example 3
Find the area of the irregular figure. Use 3.14 for p.
Step 1: Separate the figure into smaller, familiar figures.
16 m
Step 2: Find the area of each smaller figure.
9 m
Area of the parallelogram:
16 m
A = bh
Use the formula for the area of a parallelogram.
A = 16 • 9
Substitute 16 for b.
Substitute 9 for h.
A = 144

6. Example 3 Continued
Find the area of the irregular figure. Use 3.14 for p.
16 m
Area of the semicircle:
9 m
The area of a semicircle
is the area of a circle. 12
A = (pr) 1 2 __
16 m
A ≈ (3.14 • 82) 1 2 __
Substitute 3.14 for p and 8 for r.
A ≈ (200.96) 1 2 __
A ≈
Multiply.

7. Example 3 Continued
Find the area of the irregular figure. Use 3.14 for p.
Step 3: Add the area to find the total area.
16 m
9 m
A ≈ =
16 m
The area of the figure is about m2.

8. Find the area of the irregular figure. Use 3.14 for p.
Example 4
Find the area of the irregular figure. Use 3.14 for p.
Step 1: Separate the figure into smaller, familiar figures.
8 yd
Step 2: Find the area of each smaller figure.
9 yd
9 yd
Area of the rectangle:
A = lw
Use the formula for the area of a rectangle.
3 yd
A = 8 • 9
Substitute 8 for l.
Substitute 9 for w.
A = 72

9. Find the area of the irregular figure. Use 3.14 for p.
Example 4 Continued
Find the area of the irregular figure. Use 3.14 for p.
Area of the triangle:
8 yd
9 yd
The area of a triangle
is the b • h. 12
A = bh 1 2 __
9 yd
A = (3 • 9) 1 2 __
Substitute 2 for b and 9 for h.
3 yd
A = (27) 1 2 __
A = 13.5
Multiply.

10. Check It Out: Example 2 Continued
Find the area of the irregular figure. Use 3.14 for p.
Step 3: Add the area to find the total area.
A = = 85.5
The area of the figure is about 86 yd2.

11. Example 6
The Franklins want to wallpaper the wall of their daughters loft. How much wallpaper will they need?
6 ft
23 ft
18 ft
5 ft

12. Check It Out: Example 3 Continued2
Make a Plan
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.
6 ft
23 ft
18 ft
5 ft

13. Check It Out: Example 3 Continued
Solve 3
Find the area of each smaller figure.
Area of the rectangle:
Area of the triangle:
A = lw
A = bh 1 2 __
A = 18 • 6
A = (5 • 11) 1 2 __
A = 108
A = (55) 1 2 __
Add the areas to find the total area.
A = 27.5
A = = 135.5
The Franklin’s need ft2 of wallpaper.

14. Insert Lesson Title Here
Lesson Quiz
Find the area of each figure. 1. 2.
6 cm
62.13 cm2
8 cm
10 ft
84 ft2
7 ft
14 ft