Bunuel

A circle is inscribed in a square. What is the area of the shaded region?
(1) The distance from the center of the circle to a vertex of the square is \(2\sqrt{2}\)
(2) The square has a perimeter of 16.
Option D.
A) Let the radius be r and side of square be x. According to the option, r^2 + r^2 = (2*sqrt(2))^2.
r = 2. Thus, the shaded region is 4^2 - pi*(2)^2 = 4(4 - pi).
B) Let the side of the square be x. Thus, 4x = 16, x = 4. Thus, the radius of the circle is 2. Thus, the shaded region is 4^2 - pi*(2)^2 = 4(4 - pi).