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Omni-MATH / Mona has 12 match sticks of length 1, and she has to use them to make regular…

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problem

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?

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