Tadpoles

The diagram shows a shaded shape bounded by circular arcs. What is the difference in area betweeen this and the equilateral triangle shown?

Problem



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?

Image
Tadpoles


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