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 $\triangle XYZ$ ?

This problem is part of the 2018 AMC 12B .