Problem 76. Area of a Circle, Square, Circular Sector, Lune.
Level: High School, College, SAT Prep.
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. See also:
Artwork Problem
76.
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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