AMC 12 2006b Problem 16

Regular hexagon $ABCDEF$ has vertices $A$ and $C$ at $(0,0)$ and $(7,1)$, respectively. What is its area?

$\mathrm{(A)}\ 20\sqrt {3} \mathrm{(B)}\ 22\sqrt {3} \mathrm{(C)}\ 25\sqrt {3} \mathrm{(D)}\ 27\sqrt {3} \mathrm{(E)}\ 50$