<image>In the figure, equilateral hexagon $ABCDEF$ has three nonadjacent acute interior angles that each measure $30^\circ$. The enclosed area of the hexagon is $6\sqrt{3}$. What is the perimeter of the hexagon?
A. 4
B. $4\sqrt{3}$
C. 12
D. 18
E. $12\sqrt{3}$