Question

A farmer is putting up a fence for her animals. She orginally had the fence enclosing a square was 18ft by 18ft. Suppose she uses the same amount of fencing to enclose a circular area. What is the area of the circle?

Answer 1

First look: More than 324 square feet :)
Now, $l=2\pi*r$ which means that $r=\frac{l}{2\pi}$. But l is the original perimeter, 4 times the side of the square, that is, 72 ft. So, $r=\frac{72}{2\pi}=\frac{36}{\pi}$
Now, the area of that circle is $A=\pi*r^2=\pi*\frac{1296}{\pi^2}=\frac{1296}{\pi}$, which is about 412.5 square feet. It's true, that's more (that's the most you can actually get with that amount of fence :) )