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}