1. Lesson 8.5
Circles pp

2. Objectives:
1. To derive the formula for the area of a circle from the formula for the area of a regular n-gon.
2. To apply the formula to calculate areas of circles.

3. Area circle = area triangle?

4. Area circle = area square?

5. Area circle = area pentagon?

6. Area circle = area octagon?

7. Area circle = area dodecagon?

8. Area circle = area icosagon?

9. A = ap 1 2
A = rc 1 2
A = r(2r) 1 2
A = r2

10. Theorem 8.13
The area of a circle is pi times the square of the radius: A = r2.

11. Practice: Find the area of the shaded portion of the figure.2 3 6 7

12. Practice: Find the area of the shaded portion of the figure.
= 2 p = 2 1 A
A = 4(2) = 8 2 3 6
A = 7(4) = 28 7

13. Practice: Find the area of the shaded portion of the figure.
≈ 42.3 sq. units 2 3 6 7

14. Homework pp

15. ►A. Exercises Complete the table. c(units) r(units) d(units) A(units2)
1. 9
7. 30 
18 18
81 4 2 4
1.6
0.8
0.64 15 30
225
10 5 10

16. ►B. Exercises Asquare = 122 = 144 Acircle = 32 = 9
Find the area of the shaded portion.
11. 3 3
Asquare = 122
= 144
Acircle = 32
= 9 3 3
Ashaded part = 144 – 4(9) ≈ 30.9 u2

17. ►B. Exercises
Find the area of the shaded portion.
13. 12 4

18. ►B. Exercises
Find the area of the shaded portion.
15. 5 1

19. ►B. Exercises
Find the area of the shaded portion.
17. 9 4 3

20. ►B. Exercises Find the area of the shaded portion.
19. An annulus is the ring formed by two concentric circles with different radii. Derive a formula for the area of an annulus formed by two circles with radii x and y, where x  y.

21. ►B. Exercises
Find the area of the shaded portion.
19. x y

22. ►C. Exercises
20. Find the shaded area if ABCD is a square. A B C D 10

23. ►C. Exercises A B C D 10 20. Find the shaded area if ABCD is a square.

24. ►C. Exercises A B C D 10 20. Find the shaded area if ABCD is a square.

25. ►C. Exercises A B C D 10 20. Find the shaded area if ABCD is a square.

26. ►C. Exercises A B C D 10 20. Find the shaded area if ABCD is a square.

27. ■ Cumulative Review Define each. 21. Between 22. Parallelogram
23. Congruent triangles
24. Perpendicular lines
25. Median of a triangle