The diagram below shows a regular hexagonal prism (not to scale). Each side of the hexagonal faces has a length of 1 unit. The height of the prism BP is equal to the length BQ.

A slice is taken across the prism in such a way that the plane includes the line segments AB and DE. This plane also cuts the prism at points C and F. The intersection of the plane and the prism forms another hexagon ABCDEF.

Find the area of the hexagon ABCDEF.

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