Find the area of a square circumscribed around a circle of radius 18.

Since the square is circumscribed around a circle, the circle is inscribed.
The area of a square can be found through the radius of the inscribed circle using the formula:
S = 4 * r ^ 2,
where S is the area of the square, r is the radius of the circle around which the square is described.
We substitute the known value of the inscribed circle radius into the formula and find the area of the square:
S = 4 * (18 ^ 2) = 4 * 324 = 1296 (conventional square units).
Answer: S = 1296 conventional square units.