1. Break into Simpler Parts
10-3
Break into Simpler Parts
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Break into Simpler Parts
Course 1
10-3
Break into Simpler Parts
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. Break into Simpler Parts
Course 1
10-3
Break into Simpler Parts
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. Break into Simpler Parts
Course 1
10-3
Break into Simpler Parts
Learn to break a polygon into simpler parts to find its area.

5. Additional Example 1A: Finding Areas of Composite Figures
Course 1
10-3
Break into Simpler Parts
Additional Example 1A: Finding Areas of Composite Figures
Find the area of the polygon. A.
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
Course 1
10-3
Break into Simpler Parts
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 Continued
Course 1
10-3
Break into Simpler Parts
Additional Example 1B Continued
Find the area of the polygon. B.
Think: Break the figure apart into a rectangle and a triangle.
Find the area of each polygon.

8. Additional Example 1B Continued
Course 1
10-3
Break into Simpler Parts
Additional Example 1B Continued
A = bh 1 2 __
A = lw
A = • 28 • 12 1 2 __
A = 28 • 24
A = 672
A = 168
Add to find the total area of the polygon.
= 840
The area of the polygon is 840 ft2.

9. Break into Simpler Parts
Course 1
10-3
Break into Simpler Parts
Try This: Example 1A
Find the area of the polygon. A.
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. Try This: Example 1A Continued
Course 1
10-3
Break into Simpler Parts
Try This: 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. Break into Simpler Parts
Course 1
10-3
Break into Simpler Parts
Try This: Example 1B
Find the area of the polygon. B.
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. Try This: Example 1B Continued
Course 1
10-3
Break into Simpler Parts
Try This: 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 = 440
A = 176
Add to find the total area of the polygon.
= 616
The area of the polygon is 616 ft2.

13. Additional Example 2: Art Application
Course 1
10-3
Break into Simpler Parts
Additional Example 2: Art Application
Patrick made a design. All the sides are 5 inches long, except for two longer sides that are each 20 inches. All the angles are right angles. What is the area of the quilt design?
20 in.
Think: Divide the design into 3 rectangles. Find the area of one rectangle that has a length of 20 in and a width of 5 in.
5 in.
20 in.
A = lw
Write the formula.
A = 20 • 5 = 100
Multiply to find the area of the 3 rectangles.
3 • 100 = 300
The area of the design is 300 in2.

14. Break into Simpler Parts
Course 1
10-3
Break into Simpler Parts
You can also use the formula A = s2 , where s is the length of a side, to find the area of a square.
Helpful Hint

15. Break into Simpler Parts
Course 1
10-3
Break into Simpler Parts
Try This: Example 2
Yvonne made quilt design. All the sides are 4 inches long, except for the two longer sides that are each 16 inches. All the angles are right angles. What is the area of the quilt design?
Think: Divide the quilt design into 10 squares. Find the area of one square that has a side length of 4 in.
16 in.
4 in.
16 in.
A = lw
Write the formula.
A = 4 • 4 = 16
Multiply to find the area of the 10 squares.
10 • 16 = 160
The area of the quilt design is 160 in2.

16. Break into Simpler Parts Insert Lesson Title Here
Course 1
10-3
Break into Simpler Parts
Insert Lesson Title Here
Lesson Quiz
Find the area of the figure shown.
220 units2