11.6 Areas of Circles, Sectors and Segments

11.6 Areas of Circles, Sectors and Segments

Areas of Circles, Sectors and Segments Lesson 11.6 As you remember, the area of a circle is A = r2 Definition of the Area of a Sector: a region bound by 2 radii and an arc. H O

Sector HOP P O Theorem108: A sec = (mHP) 360 r Where r is the radius and the arc HP is measured in degrees.

Find the area, leave in terms of . 12m 60 A = 60(122) 360 A = 24 m2 2 Area of a segment: a segment is a region bound by a chord and its corresponding arc.

X Z The area of a segment is equal to the area of the sector - the area of the triangle. Y Given arc XY is 90 and ZX = 8 Find the shaded area. X

Segment = sector triangle = 90(82) (8) (8) Z Y 360 = 16 32 units2

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