Symbiosis National Aptitude Test SNAP 2019 Paper

Three circles of center ${\mathit{C}}_1,{\mathit{C}}_2$ and ${\mathit{C}}_3$ of radius 1 cm each are drawn such that they touch each other.

${\mathit{C}}_1{\mathit{C}}_2$ = ${\mathit{C}}_2{\mathit{C}}_3$ = ${\mathit{C}}_3{\mathit{C}}_1$ = 2 cm
∴ $\mathit{\Delta }{\mathit{C}}_1{\mathit{C}}_2{\mathit{C}}_3$ is an equilateral triangle.
Now, Area of shaded portion
= Area of $\mathit{\Delta }{\mathit{C}}_1{\mathit{C}}_2{\mathit{C}}_3$ – 3 × Area of sector ${\mathit{C}}_1$
= $\frac{\sqrt{3}}{4}\times {\left(2\right)}^2-3\times \frac{60°}{360°}\times \mathit{\pi }{\left(1\right)}^2$
= $\sqrt{3}-\frac{\mathit{\pi }}{2}$
= $\frac{\left(2\sqrt{3}-\mathit{\pi }\right)}{2}$ $\mathit{c}{\mathit{m}}^2$