ABC is an equilateral triangle. The area of the shaded region if the radius of each of the circle is 1 cm, is

The given triangle is an equilateral triangle with its edge length equal to 2 times the Radius of the circle.

= $2\times 1$cm

= 2 cm

Area of triangle = $\frac{\sqrt{3}}{4} \times$  (edge length)²

$=\frac{\sqrt{3}}{4} \times 2^2$

$=\sqrt{3}$

Area of one of the sectors $= \frac{\theta }{{360}^o} \times \pi R²$

$= \frac{60}{360} \times \pi \times {\left(1\right)}^2$

$= \frac{\pi }{6}$cm²

Area of 3 such sectors = 3  $\times \frac{\pi }{6}$ cm²

$= \frac{\pi }{2}$ cm²

Area of shaded region = Area of the triangle - Area of 3 sectors

$=\sqrt{3}-\frac{\mathrm{\pi }}{2}$ cm²