Area of a Circular Segment

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Area of a Circular Segment

• Objectives
• Review Area of Circles Sectors
• Find the Area of a Circular Segment

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Area of a Circle
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Area of a Sector
A sector is a pie-like shape of the circle, where
theta is the measure of the central angle. (a
percentage of the circle)
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Area of a Segment

• A segment is the portion of the circle with the
  radii connected at their endpoints and the
  central arc.
• (The crust of the pie slice.)

The red piece is the segment.
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Area of a Segment

• The segment is the sector minus the triangle.
• Area of a sector is .
• The area of the triangle is
• (since we know two sides and the included angle).
• Hence the area of a segment is

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Example

• Find the area of a segment of a circle whose
  diameter is 20 cm and central angle is 29 degrees.

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Practice 1

• Find the area of a circular segment to the
  nearest tenth, if the central angle is 85 degrees
  with a radius of 2.1 ft.

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Practice 2

• Find the area of a circular segment to the
  nearest tenth, if its central angle is 112.5?
  with a radius of 6 cm.

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Practice 3

• If the area of a circular segment is 54 ft.
  squared and contains a central angle of 30
  degrees, what is the value of the radius to the
  nearest tenth?