2018 AMC 12B Problem 20

Let ABCDEF be a regular hexagon with side length 1. Denote by X, Y, and Z the midpoints of sides \overline {AB}, \overline{CD}, and \overline{EF}, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of \triangle ACE and \triangle XYZ?

\textbf{(A)}\ \frac {3}{8}\sqrt{3} \qquad \textbf{(B)}\ \frac {7}{16}\sqrt{3} \qquad \textbf{(C)}\ \frac {15}{32}\sqrt{3} \qquad \textbf{(D)}\ \frac {1}{2}\sqrt{3} \qquad \textbf{(E)}\ \frac {9}{16}\sqrt{3}

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