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:
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: