Answer
The area of the circumscribed circle is twice the radius of the inscribed circle.
Work Step by Step
The circumscribed circle has a radius that is equal to half the diagonal of the square, for it touches each vertex of the square. Using 45-45-90 triangles in the square, we know that this is the same as:
$R = d/2 = \frac{s \sqrt{2}}{2}$
The radius of the inscribed circle is equal to half the length of the side. Thus, we create our proportion:
$ = \frac{ (s \sqrt{2}/2)^2}{(s/2)^2} = 2 $
