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

January 28, 2021 | education

| 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.

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