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Areas of Circles, Sectors and Segments Lesson 11.6

Areas of Circles, Sectors and Segments Lesson 11.6. As you remember, the area of a circle is. A = r 2. 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) r 2. 360.

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Areas of Circles, Sectors and Segments Lesson 11.6

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  1. Areas of Circles, Sectors and SegmentsLesson 11.6

  2. 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 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) 360 A = 24π m2 60º

  4. X Z Y 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.

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

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