GATE Civil 2023 Set 1 | GA Question: 3

Question

In the given figure, $\text{PQRSTV}$ is a regular hexagon with each side of length $5\mathrm{~cm}.$ A circle is drawn with its centre at $ \mathrm{V}$ such that it passes through $\mathrm{P}.$ What is the area $ \text{( in cm}^{2})$ of the shaded region? (The diagram is representative) 

• A. $\frac{25 \pi}{3}$ 
• B. $\frac{20 \pi}{3}$ 
• C. $6 \pi$ 
• D. $7\pi$ 

Answer 1

<PVT=120 DEGREE

FOR 360 DEGREE---→ AREA = PIE*5*5

FOR 120 DEGREEE------->X

CONVERTING IN RADIAN

X= PIE* 5 * 5 * (2*PIE/3 ) / 2*PIE

X=25 PIE/3