AMC 12 2018b 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} \textbf{(B)}\ \frac {7}{16}\sqrt{3} \textbf{(C)}\ \frac {15}{32}\sqrt{3} \textbf{(D)}\ \frac {1}{2}\sqrt{3} \textbf{(E)}\ \frac {9}{16}\sqrt{3}