Start with the area of the square.
Let s = side of square.
So, A = s^2.
A circle has a circumference.
C = 2πr
Perimeter of square = area of circle.
4s = 2πr
Solving for r, we get
4s/2π = r
2s/π = r
Ratio:
Area of square : area of circle
s^2 = πr^2
Above we solved for r. So, plug it in.
s^2 : π(2s/π)^2
s^2 : π(4s^2)/π^2
(s^2)/(4s^2)/π
(s^2) * π/(4s^2)
Answer: π/4
