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'Hexagon Cut Out' printed from http://nrich.maths.org/
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.