AMC 10 2014b Problem 13

Six regular hexagons surround a regular hexagon of side length $1$ as shown. What is the area of $\triangle{ABC}$?

$\textbf {(A) } 2\sqrt{3} \textbf {(B) } 3\sqrt{3} \textbf {(C) } 1+3\sqrt{2} \textbf {(D) } 2+2\sqrt{3} \textbf {(E) } 3+2\sqrt{3}$