Question 79578
three lines connecting the centers of the three circles form an equilateral triangle with side 12


the three "slice of pie" shaped sections in the corners of the triangle are each 1/6 of a circle


so the area of the "between" region is just the difference between the area of the triangle and 1/2 of a circle


{{{area=(1/2)b*h-(1/2)pi*r^2}}} ... {{{a=(1/2)12*6* sqrt(3)-(1/2)pi*6^2}}} ... {{{a=36*sqrt(3)-18*pi}}}