Three circles of equal radius ’a’ cm touch each other. The area of the shaded region is :

$\mathrm{AB}=\mathrm{BC}=\mathrm{CA}=2 a \mathrm{~cm} .$

$\angle \mathrm{BAC}=\angle \mathrm{ACB}=\angle \mathrm{ABC}=60^{\circ}$

Area of $\triangle \mathrm{ABC}=\frac{\sqrt{3}}{4} \times(\text { side })^{2}=\frac{\sqrt{3}}{4} \times 4 \mathrm{a}^{2}$

$=\sqrt{3} a^{2}$ sq.cm.

Area of three sectors $=3 \times \frac{60}{360} \times \pi \times a^{2}$

$=\frac{\pi a^{2}}{2}$ sq.cm.

Area of the shaded region $=\sqrt{3} a^{2}-\frac{\pi}{2} a^{2}$

$=\left(\frac{2 \sqrt{3}-\pi}{2}\right) a^{2} \text { sq.cm. }$