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Problem 76.
Area of a Circle, Square, Circular Sector, Lune.
Level: High School, SAT Prep, College |
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Given a square ABCD 1, the inscribed
circle 2, the arc BD of center A. S is the area of the lune EF, S1,
S2, and S3 are the shaded areas. Prove that S = S1 + S2 +S3.
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HINTS:
AREA OF A CIRCLE.
The area enclosed by a circle is π multiplied by the radius
squared.
CIRCULAR SECTOR: or a sector of a circle is a part of
a circle bounded by two radii and their intercepted arc.
AREA OF A CIRCULAR SECTOR: In a
circle of radius r, the area A of a sector of angle
(degrees) equals  of the area of the circle:
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