Maths Olympiad Prep

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Geometry Difficulty 4.8 AIME Prove it United States

Problem:

Mona has 1212 match sticks of length 11, 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

434=34 \frac{\sqrt{3}}{4} = \sqrt{3}.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.