Areas of Circles, Sectors Areas of Circles, Sectors and Segmentsand Segments

Lesson 11.6Lesson 11.6

A = r2

Definition of the Area of a Sector: a region bound by 2 radii and an arc.

O

H

OP

Sector HOP

As you remember, the area of a circle is

Theorem108: A sec = (mHP) r2

360

Where r is the radius and the arc HP is measured in degrees.

Find the area, leave in terms of .

12m60º

A = 60π(122) 360A = 24π m2

Area of a segment: a segment is a region bound by a chord and its corresponding arc.

X

YZ

The area of a segment is equal to the area of the sector - the area of the triangle.

X

YZ

Given arc XY is 90º and ZX = 8

Find the shaded area.Segment = sector – triangle

= 90π(82) – ½(8)(8) 360

= 16π – 32 units2