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

Area of a Circle radius

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

The red piece is the segment. 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.) radius The red piece is the segment.

Hence the area of a segment is : 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 :

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

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.

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.

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?