The diagram shows an irregular hexagon with interior angles all equal to 120 degrees made by cutting the corners off a piece of card in the shape of an equilateral triangle with sides of length 20 units.
An identical hexagon could also be made by cutting the corners off a different equilateral triangle.
What is the side length of this triangle?
If you liked this problem, here is an NRICH task
which challenges you to use similar mathematical ideas.