GATE EE 2023 Set 1 — Question 10
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.
The area of the shaded region is _______ .
The area of the shaded region is _______ .
Correct answer
(B) 18
Solution
The area of the shaded region can be found by observing the symmetry of the figure. The square has side cm, so its area is . The shaded region is formed by two semi-circles whose diameters are adjacent sides of the square. By symmetry, the shaded area is exactly half of the total area of the square. Therefore, Area .
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