The perimeter of a regular quadrilateral is 128 cm. Find the area of a circle inscribed in it.

A square is a regular quadrilateral, all sides of which are equal, and also all angles are 90 degrees.
1. The perimeter of a square with side a is found by the formula:
P = 4a,
where a is the side length of the square.
Knowing the value of the perimeter, we find the length a:
4a = 128.
By proportion:
a = 128/4;
a = 32 cm.
2. Find the radius of a circle r inscribed in a square:
r = a / 2;
r = 32/2;
r = 16 cm.
3. The area of a circle of radius r is found by the formula:
S = πr ^ 2;
S = π * 16 ^ 2 = 256π (cm ^ 2).
Answer: S = 256π cm ^ 2.