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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.

Square, Inscribed Circle, Circular Sector, Areas


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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