Chapter 11.6 Areas of Circles, Sectors, and Segments Jacob Epp Sivam Bhatt Justin Rosales Tim Huxtable

Summary In this section we will learn how to find the area of various parts of circles.

Definitions Sector - a region bounded by two radii and an arc of the circle Segment - a region bounded by a chord of the circle and its corresponding arc

There are several important formulae you will need to know for this chapter. The first is the formula for the area of a circle, which is... A = πr 2 r … radius Circles

Sectors The formula for area of a sector is … A = (M/360)πr 2 r - radius m - measure of arc

The formula for area of a segment is … A seg = A sec - A tri Segments

Segments - Step 1 1. Find the area of the sector that intercepts the segment’s arc.

Segments - Step 2 2. Find the area of the triangle formed by the two radii and the chord.

Segments - Step 3 3. Subtract the area of the triangle from the sector. minus =

Example 1: Circles Find the area of the circle with radius 7 cm. 7 cm

Solution Ex. 1 A = πr 2 A = π7 2 A = 49πcm 2

Example 2: Sectors Find the area of the sector Measure of Angle = 90 Radius = 4 4 cm. 90°

A=(M/360)πr 2 A=(90/360)π4 2 A=(1/4)π4 2 A=(1/4)16π A=4π Solution Ex. 2

Example 3: Segments Find the area of the segment. 90° 8 cm.

Solution Ex. 3 A = (M/360)πr 2 -Area of triangle A = (90/360)π8 2 -8(8)/2 A = (¼)64π-32 A = 16π-32

Example 4 Find the area of the sector AOB o A B CO

Solution to example 4 1) As you can see the radius of the circle is 12 you can find the area of the circle with πr 2. Doing so you will get the area of the circle as 144π. 2) Since the inscribed angle is 10 o arc AB would be 20 o. 3) In order to solve for this you must use the formula of a sector which is (measure of arc/360)(πr 2 ). Since we have both pieces of information we would get (1/18)(144π). Simplifying we would get 8π.

Homework Page 539 problems 1-3, 5, 11, 13-15, 18, 20