Regular Partitioning

Geometry Level 3

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 $WCXYFZ$ ?