Find the area of a square circumscribed about a circle equal to a radius of 25.

Since the square is circumscribed about a circle, the circle itself is inscribed in the square. The radius of a circle inscribed in a square is half the side of this square. Therefore, the side of the square is equal to two radii of the inscribed circle:
a = 2 * r = 2 * 25 = 50.
Now you can determine the area of the square:
S = a * a = 50 * 50 = 2500.
Answer: so the area of the square is 2500.