2016 AMC 10B Problem 23

In regular hexagon ABCDEF, points W, X, Y, and Z are chosen on sides \overline{BC}, \overline{CD}, \overline{EF}, and \overline{FA} respectively, so lines AB, ZW, YX, and ED are parallel and equally spaced. What is the ratio of the area of hexagon WCXYFZ to the area of hexagon ABCDEF?

\textbf{(A)}\ \frac{1}{3}\qquad\textbf{(B)}\ \frac{10}{27}\qquad\textbf{(C)}\ \frac{11}{27}\qquad\textbf{(D)}\ \frac{4}{9}\qquad\textbf{(E)}\ \frac{13}{27}

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