GATE 2023 EE – Question 10
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 _______ cm².
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Correct answer: (B) 18
Explanation
The two semicircles (radius 3) overlap in a lens of area $2\left(\dfrac{9\pi}{4}-\dfrac92\right)=\dfrac{9\pi}2-9$. The shaded region is the union minus the lens: $2\cdot\dfrac{9\pi}{2}-2\left(\dfrac{9\pi}2-9\right)=18$ cm².