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Areas of Circles, Sectors, and Segments

11.6

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Learning Target & Do Now

LT: Today I will be able to calculate the area of figures with rounded elements.

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DN: Given: AD || BC. What is x?

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Area of a Circle

The formula for the area of a circle should already be known

  • 𝜋r2

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Just as arcs can portion off parts of a circle, sectors portion off areas of a circle.

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Sectors

  • A sector is a region bounded by two radii and an arc of a circle
  • Just as the measure of an arc is a fraction of�the entire circle, sector area is a fraction of �circle area

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108. Asector = (Marc/360)𝜋r2

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Example

Find the area of a sector with radius 12 and a 45° arc.

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Segments of a Circle

  • Another way to partition a circle is with segments
  • A segment of a circle is the region bounded by a chord and its corresponding arc
  • How is the area of a segment found?
  • Area of the segment = Asector - Atriangle

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You Do

mAB = 90°, the radius of the circle is 10. Find the area of the segment.