2008 AMC 12B Problems/Problem 13

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

$\textbf{(A)}\ \frac{12-5\sqrt3}{72} \qquad \textbf{(B)}\ \frac{12-5\sqrt3}{36} \qquad \textbf{(C)}\ \frac{\sqrt3}{18} \qquad \textbf{(D)}\ \frac{3-\sqrt3}{9} \qquad \textbf{(E)}\ \frac{\sqrt3}{12}$

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2008 AMC 12B Problems/Problem 13