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.
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.