Hi friends,

Today I came across this question in a GMAT prep exam and I really can't figure out what I am doing wrong. I consistently arrive to answer C though I perfectly understand how to get to option E. Here is my reasoning:

Area of the circle: \(π*r^{2}\)

Area of the square:Since there are 20 meters of wire to make the square, then each side of the square must have 5 meters long.

If \(2*π*r=20\), then \(r=\frac{10}{π}\)

In order to represent the side of the square (5 meters long) in terms of \(r\), I say that \(side of the square=r*\frac{π}{2}=\frac{10}{π}*\frac{π}{2}=5\). So \(area of the square=(r*\frac{π}{2})^2=\frac{1}{4}∗π^2∗r^2\)

Total area: \(πr^{2}+\frac{1}{4}∗π^2∗r^2\)

Option C

It would help me a lot if somebody could tell me where is the flaw in my method.