Acircle is inscribed in a square. write and simplify an expression for the ratio of the area of the square to the area of the circle. for a circle inscribed in a square, the diameter of the circle is equal to the side length of the square.

Given:
circle inscribed in a square.
Side length of the square = diameter of the circle.
Let x side length and diameter.

Area of a square = x²

Area of a circle = πr²

r = radius ; half of the diameter. = x/2

Area of a circle = π * (x/2)²  or π (x²/4)

Ratio of the area of the square to the area of the circle

x² : π(x²/4)   or x² / πx²/4

x² * 4/πx² = 4/π

The area of a circle with a diameter d is  and the area of a square whose side is the diameter d of the circle is .
The ratio of the area of a square to the area of a circle is

Since there is a common term on both sides, we cancel  and get the final ratio of: