The convex pentagon ABCDE has ∠A=∠B=120∘, EA=AB=BC=2 and CD=DE=4. What is the area of ABCDE?
[asy]
draw((0,0)--(1,0)--(1.5,sqrt(3)/2)--(0.5,3sqrt(3)/2)--(-0.5,sqrt(3)/2)--cycle);
dot((0,0));
dot((1,0));
dot((1.5,sqrt(3)/2));
dot((0.5,3sqrt(3)/2));
dot((-0.5,sqrt(3)/2));
label("A", (0,0), SW);
label("B", (1,0), SE);
label("C", (1.5,sqrt(3)/2), E);
label("D", (0.5,3sqrt(3)/2), N);
label("E", (-.5, sqrt(3)/2), W);
[/asy]
<spanclass=′latex−bold′>(A)</span>10<spanclass=′latex−bold′>(B)</span>73<spanclass=′latex−bold′>(C)</span>15<spanclass=′latex−bold′>(D)</span>93<spanclass=′latex−bold′>(E)</span>125