In a regular hexagon $ABCDEF$, points $W$, $X$, $Y$, and $Z$ are on sides $CD$, $BC$, $AF$, and $EF$, respectively, in a way such that $AB$, $WZ$, $XY$, and $ED$ are parallel and equidistant. If the side length of $ABCDEF$ is 1, what is the area of hexagon $WCXYFZ$?
