## Feynman Parallelogram Variation

For a parallelogram *ABCD* in the plane, if each side is divided by a point (1/*p*), (*p* >= 2) (measured say anti-clockwise), find a formula relating the area of *ABCD* with that of *A'B'C'D'* (parallelogram formed by these points).

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Feynman Parallelogram Variation: 1/2 division

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Feynman Parallelogram Variation: 1/3 division

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Feynman Parallelogram Variation: 1/4 division

Can you generalize even further for sides divided into different ratios?

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Michael de Villiers, Sept 2009.