1. Area of Composite Figures
10-3
Area of Composite Figures
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
1. What is the area of a rectangle with length 10 cm and width 4 cm?
2. What is the area of a parallelogram with base 18 ft and height 12 ft?
3. What is the area of a triangle with base 16 cm and height 8 cm?
40 cm2
216 ft2
64 cm2

3. Problem of the Day
Four squares are stacked in a tower. The bottom square is 12 inches on a side. The perimeter of each of the other squares is half of the one below it. What is the perimeter of the combined figure?
69 in.

4. Learn to break a polygon into simpler parts to find its area.

5. Additional Example 1A: Finding Areas of Composite Figures
Find the area of the polygon.
1.7 cm
4.9 cm
1.3 cm
2.1 cm
Think: Break the polygon apart into rectangles.
Find the area of each rectangle.

6. Additional Example 1A Continued
1.7 cm
4.9 cm
1.3 cm
2.1 cm
A = lw
A = lw
Write the formula for the area of a rectangle.
A = 4.9 • 1.7
A = 2.1 • 1.3
A = 8.33
A = 2.73
= 11.06
Add to find the total area.
The area of the polygon is cm2.

7. Additional Example 1B: Finding Areas of Composite Figures
Find the area of the polygon.
Think: Break the figure apart into a rectangle and a triangle.
Find the area of each polygon.

8. Additional Example 1B Continued
A = bh 1 2 __
A = lw
A = • 28 • 12 1 2 __
A = 28 • 24
A = 168
A = 672
Add to find the total area of the polygon.
= 840
The area of the polygon is 840 ft2.

9. Check It Out: Example 1A
Find the area of the polygon.
1.9 cm
1.9 cm
5.5 cm
5.5 cm
1.5 cm
1.5 cm
2 cm
2 cm
3.4 cm
Think: Break the polygon apart into rectangles.
Find the area of each rectangle.

10. Check It Out: Example 1A Continued
1.9 cm
5.5 cm
1.5 cm
2 cm
A = lw
A = lw
Write the formula for the area of a rectangle.
A = 5.5 • 1.9
A = 2 • 1.5
A = 10.45
A = 3
= 13.45
Add to find the total area.
The area of the polygon is cm2.

11. Check It Out: Example 1B
Find the area of the polygon.
20 ft
22 ft
16 ft
36 ft
20 ft
22 ft
Think: Break the figure apart into a rectangle and a triangle.
Find the area of each polygon.

12. Check It Out: Example 1B Continued
16 ft
20 ft
22 ft
22 ft
A = bh 1 2 __
A = lw
A = • 22 • 16 1 2 __
A = 22 • 20
A = 176
A = 440
Add to find the total area of the polygon.
= 616
The area of the polygon is 616 ft2.

13. Additional Example 2: Art Application
Patrick made a design. Use the coordinate grid to find its area.
Think: Divide the design into rectangles. Find the area of each rectangle.
Rectangle 1
l = 5, w = 5; A = 5 • 5 = 25 25 20
Rectangle 2 15
l = 10, w = 5; A = 10 • 5 = 50 10
Rectangle 3 5
l = 15, w = 5; A = 15 • 5 = 75 5 10 15 20 25
Rectangle 4
l = 20, w = 5; A = 20 • 5 = 100

14. Additional Example 2 Continued
Add the areas of the four rectangles to find the total area of the design.
= 250 square units.
The area of the design is 250 square units.

15. You can also count the squares and multiply by the area of one square
You can also count the squares and multiply by the area of one square. 1 square = 25 square units. 10 • 25 = 250 square units.
Helpful Hint

16. Lawanda made a design. Use the coordinate grid to find its area.
Check It Out: Example 2
Lawanda made a design. Use the coordinate grid to find its area.
Think: Divide the design into rectangles. Find the area of each rectangle.
Rectangle 1 25
l = 5, w = 10; A = 5 • 10 = 50 20 1 15 2
Rectangle 2 10 3
l = 5, w = 15; A = 5 • 15 = 75 5
Rectangle 3 5 10 15 20 25
l = 5, w = 10; A = 5 • 10 = 50

17. Check It Out: Example 2 Continued
Add the areas of the three rectangles to find the total area of the design.
= 175 square units.
The area of the design is 175 square units.

18. Lesson Quiz
1. Find the area of the figure shown.
220 units2
2. Phillip designed a countertop. Use the coordinate grid to find its area.
30 units2