Correct Answer - Option 2 :
\(\left( \sqrt 3- \frac{\pi}{2} \right)\) sq.cm.
Given:
Radius of coin = 1 cm
Formula Used:
Area of minor sector = \(\frac{A}{360} × πr^2\)
Area of equilateral triangle = \(\frac{√3}{4} × (Side)^2\)
Calculation:
Radius of each coin = 1 cm
With all three centers, an equilateral triangle of side 2 cm is formed.
The area enclosed by coin = Area of an equilateral triangle - 3 × Area of a sector of angle 60°
⇒ The area enclosed by coins = \(\frac{√3}{4}(2)^2 - 3 \times \frac{60}{360}\times π(1)^2\)
⇒ The area enclosed by coins = \((√3 - \frac{π}{2}) cm^2\)
∴ The area enclosed by coins is \((√3 - \frac{π}{2}) cm^2\)
The correct option is 2 i.e. \((√3 - \frac{π}{2}) cm^2\)