UPSC CDS 2 2022 Math Paper

Radius of inscribed circle (r)=‌

‌ side ‌

2√3

Area of equilateral triangle =‌

√3

4

(‌ side ‌)2
Area of circle =πr2
We have,
Radius of circle =‌

2√3

2√3

=1‌cm
Area of shaded region = Area of an equilateral triangle − Area of a circle
Area of shaded region =‌

√3

4

(2√‌3)2−π(1)2
Area of shaded region =‌

√3

4

×4×3−π
Area of shaded region =(3√‌3−π)cm2