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.
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.
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?
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.