1979 AHSME Problem 10

If P_1P_2P_3P_4P_5P_6 is a regular hexagon whose apothem (distance from the center to midpoint of a side) is 2, and Q_i is the midpoint of side P_iP_{i+1} for i=1,2,3,4, then the area of quadrilateral Q_1Q_2Q_3Q_4 is

\textbf{(A) }6\qquad \textbf{(B) }2\sqrt{6}\qquad \textbf{(C) }\frac{8\sqrt{3}}{3}\qquad \textbf{(D) }3\sqrt{3}\qquad \textbf{(E) }4\sqrt{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.