How to find the areas of circles, sectors, and segments of circles. Chapter 10.7GeometryStandard/Goal 2.2

1. Check and discuss the assignment from yesterday. 2. Read, write, and discuss how to find the areas of circles, sectors, and segments of circles. 3. Work on assignment.

The area of a circle is the product of and the square of the radius r

Sector of a circle is the region bounded by an arc of the circle and the two radii to the arc’s endpoint.

The ratio of the area A of a sector of a circle to the area of the circle is equal to the ratio of the measure of the intercepted arc to 360˚ B A P r

Segment of a circle a part of a circle bounded by an arc and the segment joining its endpoints. Segment of a circle

Because the diameters are in different units, convert 1 ft to 12 in. The radius of the archery target is 1 ft = 12 in. The area of the archery target is r 2 = (12) 2 = 144 in. 2 A circular archery target has a 2-ft diameter. It is yellow except for a red bull’s-eye at the center with a 6-in. diameter. Find the area of the yellow region. Round your answer to the nearest whole number. Find the areas of the archery target and the bull’s-eye. The radius of the archery target is = 1 ft Lesson 10-7

The area of the red region is r 2 = (3) 2 = 9 in. 2 The radius of the red region is = 3 in (continued) Use a calculator The area of the yellow region is about 424 in. 2 area of archery target – area of red region = area of yellow region 144 –9 =135 Lesson 10-7

The area of sector ACB is 10 m 2. = 10 = = (6) Find the area of sector ACB. Leave your answer in terms of. area of sector ACB = r 2 mAB 360 Lesson 10-7

= (24) 2 Substitute = 576 = 192 Simplify area of sector AOB = r 2 Use the formula for area of a sector. mAB 360 Lesson 10-7 Find the area of the shaded segment. Round your answer to the nearest tenth. Step 1: Find the area of sector AOB.

A = bh Area of a triangle A = (24 3 )(12)Substitute 24 for b and 12 for h. A = 144 3Simplify You can use a 30°-60°-90° triangle to find the height h of AOB and AB. 24 = 2 h hypotenuse = 2 shorter leg 12 = h Divide each side by 2. = 3 12 = 12 3longer leg = 3 shorter leg AB = 24 3Multiply each side by 2. AB 2 (continued) Step 2: Find the area of AOB. AOB has base 12 3 ft ft, or 24 3 ft and height 12 ft. Lesson 10-7

area of segment = 192 – To the nearest tenth, the area of the shaded segment is ft Use a calculator. Step 3: Subtract the area of AOB from the area of sector AOB to find the area of the segment of the circle. (continued) Lesson 10-7

Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.