2009 Gauss 8 Problem 20

A piece of string fits exactly once around the perimeter of a square whose area is 144. Rounded to the nearest whole number, the area of the largest circle that can be formed from the piece of string is

\textbf{(A)}\ 144\quad \textbf{(B)}\ 733\quad \textbf{(C)}\ 113\quad \textbf{(D)}\ 452\quad \textbf{(E)}\ 183

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.