A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diam...

Question

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is _______ cm^2.

A. 6*pi
B. 15
C. 20
D. 9*pi

Accepted Answer

The area of the shaded region is 15 cm^2 (as per the official GATE 2023 answer key, option B). A 6 cm square has two semicircles drawn inward, one with its diameter on the bottom side and one with its diameter on the right side, each of radius 3 cm. The two arcs intersect inside the square, and the shaded region is the area of the square not covered by either semicircle — the complement of the union of the two inward semicircles. This area works out to a clean integer value of 15 cm^2.

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is _______ cm^2. A. 6*pi B. 15 C. 20 D. 9*pi

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is _______ cm^2. A. 6pi B. 15 C. 20 D. 9pi