2012 AMC 12B Problem 10

What is the area of the polygon whose vertices are the points of intersection of the curves x^2 + y^2 =25 and (x-4)^2 + 9y^2 = 81?

\textbf{(A)}\ 24\qquad\textbf{(B)}\ 27\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 37.5\qquad\textbf{(E)}\ 42

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.