1. Areas of Circles, Sectors and Segments Lesson 11.6

2. As you remember, the area of a circle is
Definition of the Area of a Sector: a region bound by 2 radii and an arc. H
Sector HOP O P O

3. 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 .
12m
A = 60π(122)
A = 24π m2
60º

4. Area of a segment: a segment is a region bound by a chord and its corresponding arc.
The area of a segment is equal to the area of the sector - the area of the triangle. X Y Z

5. Given arc XY is 90º and ZX = 8 Find the shaded area. X Z Y
Segment = sector – triangle
= 90π(82) – ½(8)(8)
= 16π – 32 units2 X Y Z