Find The Area

Geometry Level 2

The rectangle $$ABCD$$ is twice as wide as it is high. Parallel lines which are a distance of $$p$$ apart cross the mid-point of the long sides of the rectangle at $$e$$ and $$f$$ as shown. All 3 regions (red, green, blue) are of equal area.

What is the area of the rectangle $$ABCD$$ as a function of $$p$$?

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