AMC 10 2014a Problem 13

Equilateral $\triangle ABC$ has side length $1$, and squares $ABDE$, $BCHI$, $CAFG$ lie outside the triangle. What is the area of hexagon $DEFGHI$?

$\textbf{(A)}\ \dfrac{12+3\sqrt3}4 \textbf{(B)}\ \dfrac92 \textbf{(C)}\ 3+\sqrt3 \textbf{(D)}\ \dfrac{6+3\sqrt3}2 \textbf{(E)}\ 6$