1999 AHSME Problem 23

The equiangular convex hexagon ABCDEF has AB = 1, BC = 4, CD = 2, and DE = 4. The area of the hexagon is

\mathrm{(A) \ } \frac {15}2\sqrt{3} \qquad \mathrm{(B) \ }9\sqrt{3} \qquad \mathrm{(C) \ }16 \qquad \mathrm{(D) \ }\frac{39}4\sqrt{3} \qquad \mathrm{(E) \ } \frac{43}4\sqrt{3}

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