olymmath

HMMT 2001 U27

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Mona has 12 match sticks of length 1 , and she has to use them to make regular polygons, with each match being a side or a fraction of a side of a polygon, and no two matches overlapping or crossing each other. What is the smallest total area of the polygons Mona can make?

Dataset text NuminaMath olympiads. Quoted with source.

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\sqrt{3}

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