2008 AMC 12B Problem 13

Vertex E of equilateral triangle \triangle ABE is in the interior of unit square ABCD. Let R be the region consisting of all points inside ABCD and outside \triangle ABE whose distance from \overline{AD} is between \frac{1}{3} and \frac{2}{3}. What is the area of R?

\textbf{(A)}\ \frac{12-5\sqrt{3}}{72} \qquad \textbf{(B)}\ \frac{12-5\sqrt{3}}{36} \qquad \textbf{(C)}\ \frac{\sqrt{3}}{18} \qquad \textbf{(D)}\ \frac{3-\sqrt{3}}{9} \qquad \textbf{(E)}\ \frac{\sqrt{3}}{12}

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