OpenSAT

The area of the square is 64, so the side length of the square is 8. The diagonal of the square is equal to the diameter of the circle. Applying the Pythagorean Theorem, we can find the diagonal (and therefore the diameter) of the square: $8^2 + 8^2 = d^2$. This simplifies to $128 = d^2$, which means the diameter is $\sqrt{128} = 8\sqrt{2}$. The radius of the circle is half the diameter, so the radius is $4\sqrt{2}$. The area of the circle is $\pi r^2$, so the area is $\pi (4\sqrt{2})^2 = \pi (16 \cdot 2) = \pi (32) = 16 \pi$.