AHSME 1993 Problem 14

The convex pentagon $ABCDE$ has $\angle{A}=\angle{B}=120^\circ,EA=AB=BC=2$ and $CD=DE=4$. What is the area of ABCDE? $\text{(A) } 10 \text{(B) } 7\sqrt{3} \text{(C) } 15 \text{(D) } 9\sqrt{3} \text{(E) } 12\sqrt{5}$