Three circles of equal radius 'r' cm touch each other.  The area of shaded region is?

\(\frac{2\sqrt {3}-π}{2}\) r² sq. cm

Joining centres of three circles we get equilateral triangle ABC

AB = AC = BC = 2r

shaded area = Ar. of equi ΔABC - Ar. of 3 sectors inside the ΔABC

                 = \(\frac{\sqrt {3}}{4}\) × (side)² - 3 × ( πr² \(\frac{θ}{360}\) )

                 =  \(\frac{\sqrt {3}}{4}\) (2r)² - 3 × (πr² \(\frac{60}{360}\))

                 =  \(\frac{\sqrt {3}}{1}\) r² - \(\frac{πr^2}{2}\) 

                 =  \(\frac{2\sqrt {3} - π}{2}\) r² sq. cm