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United States competition problems

Geometry Difficulty 4.8 AIME Prove it United States

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?

Solution

$4 \frac{\sqrt{3}}{4} = \sqrt{3}$ .

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