1. Area of Irregular Figures
9-6
Area of Irregular Figures
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Area of Irregular Figures
Course 2
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
yd2

3. Area of Irregular Figures
Course 2
9-6
Area of Irregular Figures
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?
3 4
11 ft; 22 ft; 33 ft

4. Area of Irregular Figures
Course 2
9-6
Area of Irregular Figures
Learn to find the area of irregular figures.

5. 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.

6. Additional Example 1: Estimating the Area of an Irregular Figure
Course 2
9-6
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: 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.

7. Area of Irregular Figures
Course 2
9-6
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) = =15.
1 2
The area of the figure is about 15 yd . 2

8. Additional Example 2: Finding the Area of an Irregular Figure
Course 2
9-6
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 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

9. Additional Example 2 Continued
Course 2
9-6
Area of Irregular Figures
Additional Example 2 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.

10. Additional Example 2 Continued
Course 2
9-6
Area of Irregular Figures
Additional 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.
16 m
9 m
A ≈ =
16 m
The area of the figure is about m2.

11. Area of Irregular Figures
Course 2
9-6
Area of Irregular Figures
Check It Out: Example 2
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

12. Check It Out: Example 2 Continued
Course 2
9-6
Area of Irregular Figures
Check It Out: Example 2 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 = (2 • 9) 1 2 __
Substitute 2 for b and 9 for h.
2 yd
A = (18) 1 2 __
A = 9
Multiply.

13. Check It Out: Example 2 Continued
Course 2
9-6
Area of Irregular Figures
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 = = 81
The area of the figure is about 81 yd2.

14. Additional Example 3: Problem Solving Application
Course 2
9-6
Area of Irregular Figures
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

15. Understand the Problem
Course 2
9-6
Area of Irregular Figures
Additional Example 3 Continued 1
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.

16. Additional Example 3 Continued
Course 2
9-6
Area of Irregular Figures
Additional Example 3 Continued 2
Make a Plan
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.
5 ft
8 ft
4 ft
7 ft t

17. Additional Example 3 Continued
Course 2
9-6
Area of Irregular Figures
Additional Example 3 Continued
Solve 3
Find the area of each smaller figure.
Area of the rectangle:
Area of the trapezoid:
A = lw
A = h(b1 + b2) 1 2 __
A = 8 • 5
A = • 4(5 + 7) 1 2 __
A = 40
A = • 4 (12) 1 2 __
Add the areas to find the total area.
A = 24
A = = 64
The Wrights’ need 64 ft2 of tile.

18. Additional Example 3 Continued
Course 2
9-6
Area of Irregular Figures
Additional Example 3 Continued 4
Look Back
The area of the entry must be greater than the area of the rectangle (40 ft2), so the answer is reasonable.

19. Area of Irregular Figures
Course 2
9-6
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 ft
5 ft

20. Understand the Problem
Course 2
9-6
Area of Irregular Figures
Check It Out: Example 3 Continued 1
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.

21. Check It Out: Example 3 Continued
Course 2
9-6
Area of Irregular Figures
Check It Out: Example 3 Continued 2
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

22. Check It Out: Example 3 Continued
Course 2
9-6
Area of Irregular Figures
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.

23. Check It Out: Example 3 Continued
Course 2
9-6
Area of Irregular Figures
Check It Out: Example 3 Continued 4
Look Back
The area of the wall must be greater than the area of the rectangle (108 ft2), so the answer is reasonable.

24. Area of Irregular Figures Insert Lesson Title Here
Course 2
9-6
Area of Irregular Figures
Insert Lesson Title Here
Lesson Quiz
Find the perimeter and area of each figure. 1. 2.
6 cm
31.42 cm, cm2
8 cm
10 ft
39.1 ft, 84 ft2
7 ft
14 ft