Lesson 8.5 Circles pp. 338-340.

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Presentation transcript:

Lesson 8.5 Circles pp. 338-340

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.

Area circle = area triangle?

Area circle = area square?

Area circle = area pentagon?

Area circle = area octagon?

Area circle = area dodecagon?

Area circle = area icosagon?

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

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

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

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

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

Homework pp. 339-340

►A. Exercises Complete the table. c(units) r(units) d(units) A(units2) 1. 9 3. 4 5. 1.6 7. 30 9. 25 18 18 81 4 2 4 1.6 0.8 0.64 15 30 225 10 5 10

►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

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

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

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

►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.

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

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

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

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

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

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

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