2012 Fermat Problem 13

The diagram shows a square quilt that is made up of identical squares and two sizes of right-angled isosceles triangles. What percentage of the quilt is shaded?

\textbf{(A)}\ 36\%\quad \textbf{(B)}\ 40\%\quad \textbf{(C)}\ 44\%\quad \textbf{(D)}\ 48\%\quad \textbf{(E)}\ 50\%

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 Fermat contests here.