Section 7-7: Circles: Area of circles, sectors, and segments

April 10, 2012

Warm-up: (20 mins)

Create your own figure using a circle and at least 2 other types of shapes. Include at least 5 shapes.

Swap with your partner. Find the perimeter/circumference

of the figure. Check each other’s work.

Questions on Homework?

Section 7-7 Circles: Area of circles,

sectors, and segments

Objective: Today you will learn to find areas of circles sectors segments

Area of a Circle

Area of a parallelogram = b*h = ½ C*r C = 2πrArea of a circle = ½ (2πr)*r = πr2

Area of our cookie cake is ____________.

Example 1:

Find the exact area of these circles

1. 2.

3. d = 16 ft 4. r = 5.3 cm

Example 2: What is the radius of a circle with area = 144πm2?

Area of a Sector:

How big is your piece of the pie?

Sector – region bounded by two radii and their intercepted arc

Area of sector = * area of circle

Example 3: Find the area of shaded sector

Example 4: Find area of sectors with the

given information:

a) mXY = 720; r = 20cm

b) mMN = 1200; r = 6 ft

c) mAB = 1500; d = 8 in

Example 5: Find areas in terms of π

Circle A =

Sector CD =

Sector DEC =

Sector CDE =

Sector ED =

Sector CD + Sector DEC =

Segment of a circle

Segment of a circle – region of a circle bounded by an arc and the segment joining its endpoints

Area of a Segment of a circle

Area of sector - Area of triangle = Area of segment

Example 6: Find area of shaded segment. Round your answer to the nearest tenth.

Example 7: Find area of shaded segment. Round your answer to the nearest tenth.

Example 7 (cont’d): Find area of shaded segment. Round your answer to the nearest tenth.

Example 7 (cont’d): Find area of shaded segment. Round your answer to the nearest tenth.

Example 8: Find area of shaded segment. Round your answer to the nearest tenth.

Example 9: Find area of shaded segment. Round your answer to the nearest tenth.

Example 10: Find area of shaded segments. Round your answer to the nearest hundredth.

Given: • AD = 8√3• m∠AEF = 600

Wrap-up Today you learned to find areas of

circles sectors segments

Tomorrow you will learn about Geometric Probability

Homework (H) p. 397 # 1 - 11, 17 – 19, 22, 23, 25, 27, 32, 35Homework (R) p. 397 # 1 - 11, 17 – 19, 22, 25, 26, 27, 28, 35