Let A B C D E F be a regular hexagon with side length 1 . Denote by X, Y, and Z the midpoints of sides \overline{A B}, \overline{C D}, and \overline{E F}, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of \triangle A C E and \triangle X Y Z ?

**Answer Choices**

A. \dfrac{3}{8} \sqrt{3}

B. \dfrac{7}{16} \sqrt{3}

C. \dfrac{15}{32} \sqrt{3}

D. \dfrac{1}{2} \sqrt{3}

E. \dfrac{9}{16} \sqrt{3}