Let the area of the square be represented by A. Then one side of the square is √A, and the diagonal of the square (the diameter of the circle) is √(2A).

The area of a circle is

area = π(d/2)^2 = (π/4)d^2

Our circle has diameter d = √(2A), so the area of our circle is

area = (π/4)(√(2A))^2

= 2πA/4

= (π/2)A

The area of a circle is

area = π(d/2)^2 = (π/4)d^2

Our circle has diameter d = √(2A), so the area of our circle is

area = (π/4)(√(2A))^2

= 2πA/4

= (π/2)A