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?

Problem



Image
Hexagon Cut Out


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.