SSC CGL 2025 PYQ — Question 58

The correct answer is option 1 i.e. 166 cm².

For an equilateral triangle, inradius r = $a\sqrt{3} \over 6$

⇒ a = $6r \over \sqrt{3}$

⇒ a = $18 \sqrt{3}$

Now, area of equilateral triangle = $\frac{\sqrt{3}}{4} a^2$

⇒ $\frac{\sqrt{3}}{4} \times (18 \sqrt{3})^2$

⇒ $\frac{\sqrt{3}}{4} \times (324\times3)$ = $243\sqrt{3}$

Area of circle = $\pi r^2$

⇒ $\pi \times 9^2$ = $81\pi$

Remaining area = $243\sqrt{3}$ - $81\pi$

⇒ 420.88 - 254.58 = 166.30 ≈ 166