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Intersecting Squares

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April 2, 2013
geometry

Problem Statement

The vertex EE of a square EFGHEFGH is at the center of square ABCDABCD. The length of a side of ABCDABCD is 11 and the length of a side of EFGHEFGH is 22. Side EFEF intersects CDCD at II and EHEH intersects ADAD at JJ. If angle EID=60∘EID=60^\circ, the area of quadrilateral EIDJEIDJ is
<spanclass=′latex−bold′>(A)</span>14<spanclass=′latex−bold′>(B)</span>36<spanclass=′latex−bold′>(C)</span>13<spanclass=′latex−bold′>(D)</span>24<spanclass=′latex−bold′>(E)</span>32<span class='latex-bold'>(A) </span>\dfrac14\qquad<span class='latex-bold'>(B) </span>\dfrac{\sqrt3}6\qquad<span class='latex-bold'>(C) </span>\dfrac13\qquad<span class='latex-bold'>(D) </span>\dfrac{\sqrt2}4\qquad<span class='latex-bold'>(E) </span>\dfrac{\sqrt3}2
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