Vertex E of equilateral \triangle A B E is in the interior of unit square A B C D. Let R be the region consisting of all points inside A B C D and outside \triangle A B E whose distance from \overline{A D} is between \dfrac{1}{3} and \dfrac{2}{3}. What is the area of R ?
Answer Choices
A. \dfrac{12-5 \sqrt{3}}{72}
B. \dfrac{12-5 \sqrt{3}}{36}
C. \dfrac{\sqrt{3}}{18}
D. \dfrac{3-\sqrt{3}}{9}
E. \dfrac{\sqrt{3}}{12}