The perimeter of the square is 48 cm *. Determine the area of the circle inscribed in this circle.

1. Since all sides of the square are equal, the perimeter of the square is:
P = t + t + t + t = 4t,
where t is the length of the side of the square.
4t = 48;
t = 48/4;
t = 12 cm.
2. The radius of a circle inscribed in a square is found by the formula:
r = t / 2.
r = 12/2;
r = 6 cm.
3. The area of a circle of radius r is found by the formula:
S = πr ^ 2;
S = 6 ^ 2 * π;
S = 36π cm.
Answer: S = 36π cm.