Areas of Circles, Sectors and Segments Lesson 11.6

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Areas of Circles, Sectors and Segments Lesson 11.6

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

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) 360 A = 24π m2 60º

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

Given arc XY is 90º and ZX = 8 Find the shaded area. X Z Y Segment = sector – triangle = 90π(82) – ½(8)(8) 360 = 16π – 32 units2 X Y Z