What is the area of circle whose radius is the diagonal of a square and whose area is 4?

Answer 1

To find the area of the circle, we first determine the radius of the square. If the area of the square is 4, the side length is ( \sqrt{4} = 2 ). The diagonal ( d ) of the square can be found using the formula ( d = s\sqrt{2} ), where ( s ) is the side length. Thus, the diagonal is ( 2\sqrt{2} ), which serves as the radius of the circle. The area of the circle is given by ( A = \pi r^2 = \pi (2\sqrt{2})^2 = 8\pi ).