What is the area of a square with a circle of a radius of 5 inches?

Answer 1

If the circle is inscribed in the square, the side length of the square is the same as the diameter of the circle which is twice its radius:

→ area_square = (2 × 5 in)² = 10² sq in = 100 sq in

If the circle circumscribes the square, the diagonal of the square is the same as the diameter of the circle; Using Pythagoras the length of the side of the square can be calculated:

→ diagonal = 2 × 5 in = 10 in

→ side² + side² = diagonal²

→ 2 × side² = diagonal²

→ side² = diagonal² / 2

→ side = diagonal / √2

→ side = 10 in / √2

→ area _square = (10 in / √2)² = 100 sq in / 2 = 50 sq in.

Answer 2

If the circle is inscribed in the square, the side length of the square is the same as the diameter of the circle - which in turn is twice the radius.