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Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

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LOGO Challenge 6 - Triangles and Stars

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

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Hexagon Cut Out

Weekly Problem 52 - 2012
An irregular hexagon can be made by cutting the corners off an equilateral triangle. How can an identical hexagon be made by cutting the corners off a different equilateral triangle?


Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
See all short problems arranged by curriculum topic in the short problems collection

The diagram shows a regular pentagon and regular hexagon which overlap. What is the value of $x$?


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.



This problem is taken from the UKMT Mathematical Challenges.