GATE CE 2023 Set 1 — Question 3
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. What is the area (in ) of the shaded region? (The diagram is representative)
📷 Figure: A regular hexagon PQRSTV with a circle centered at V passing through P. The sector PVT inside the hexagon is shaded.
Correct answer
(A) (25π)/(3)
Solution
1.In a regular hexagon, the interior angle at each vertex is given by .
2.The circle is centered at vertex and passes through vertex . Since and are adjacent vertices in the hexagon, the radius of the circle is equal to the side length of the hexagon, cm.
3.The shaded region is the sector of the circle that lies inside the hexagon. The central angle of this sector is the interior angle of the hexagon at vertex , which is .
4.The area of a sector is given by . Substituting the values: Area .
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