AHSME 1999 Problem 23

The equiangular convex hexagon $ABCDEF$ has $AB = 1, BC = 4, CD = 2,$ and $DE = 4.$ The area of the hexagon is $\mathrm{(A) \ } \frac {15}2\sqrt{3} \mathrm{(B) \ }9\sqrt{3} \mathrm{(C) \ }16 \mathrm{(D) \ }\frac{39}4\sqrt{3} \mathrm{(E) \ } \frac{43}4\sqrt{3}$

Solution