AMC 8 2012 Problem 23

An equilateral triangle and a regular hexagon have equal perimeters. If the triangle's area is 4, what is the area of the hexagon? $\textbf{(A)}\hspace{.05in}4 \textbf{(B)}\hspace{.05in}5 \textbf{(C)}\hspace{.05in}6 \textbf{(D)}\hspace{.05in}4\sqrt3 \textbf{(E)}\hspace{.05in}6\sqrt3$