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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