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The diagram shows a shaded shape bounded by circular arcs with the same radius. The centres of three arcs are the vertices of an equilateral triangle; the other three centres are the midpoints of the sides of the triangle. The sides of the triangle have length 2.

What is the difference between the area of the shaded shape and the area of the triangle?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

*This problem is taken from the UKMT Mathematical Challenges.*