Find the area of the Reuleaux triangle given below. The radius of each circle is 1.
The area of the triangle (not counting the circular segments) is: A = sqrt(3)/4·12 = sqrt(3)/4.
Since the triangle is an equilateral triangle, each arc is 60o.
The area of one sector of the circle is one-sixth of the circle: A = (1/6)·pi·12 = (1/6)·pi
If you add three of these together, you get (1/2)·pi.
However, this means that you have counted the area of the triangle 3 times, so you'll need to subtract
two of those triangles: (1/2)·pi. - 2·sqrt(3)/4