2002 AMC 10P Problem 14

The vertex E of a square EFGH is at the center of square ABCD. The length of a side of ABCD is 1 and the length of a side of EFGH is 2. Side EF intersects CD at I and EH intersects AD at J. If angle EID=60^{\circ}, the area of quadrilateral EIDJ is

\text{(A) }\frac{1}{4} \qquad \text{(B) }\frac{\sqrt{3}}{6} \qquad \text{(C) }\frac{1}{3} \qquad \text{(D) }\frac{\sqrt{2}}{4} \qquad \text{(E) }\frac{\sqrt{3}}{2}

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