Hexagon Area given Width

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A convex hexagon, with parallel opposite sides has three different widths [distance between opposite parallel sides]. Given widths A,B and C, what is the hexagons area, in a general form that works for unequal A,B and C?

The constraints of parallel opposite sides means that each opposite side is of equal length, but I have been unable to use this information to determine area.

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three widths fixed

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