Regular Partitioning

Geometry Level 3

In a regular hexagon ABCDEFABCDEF, points WW, XX, YY, and ZZ are on sides CDCD, BCBC, AFAF, and EFEF, respectively, in a way such that ABAB, WZWZ, XYXY, and EDED are parallel and equidistant. If the side length of ABCDEFABCDEF is 1, what is the area of hexagon WCXYFZWCXYFZ?

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