A square ABCD is inscribed in a circle of radius r.

Let the diameter of the square be d and having circumscribed circle of radius r.
We know that if a circle circumscribes a square, then the diameter of the circle is equal to the diagonal of the square.
∴ d = 2r
Now,

Area of square $=\frac{1}{2} d^{2}=\frac{1}{2}(2 r)^{2}=2 r^{2}$ sq units

Hence, the area of the square ABCD is 2r2 sq units.