PareshGmat wrote:
ABCD is a square. If the shaded area is A, the side of the square is:
The moment I see a variable in the options, my instinct is to assume a value.
For ease, I say the side of the square is 2 which means the diameter of the circle is 2. So the radius of the circle is 1.
A quarter of the square will have area \(1^2 = 1\) and a quarter of the circle will have area \(\frac{\pi*r^2}{4} = \frac{\pi}{4}\).
\(A = 1 - \frac{\pi}{4} = \frac{(4 - \pi)}{4}\)
Now look for the option in which if you put this value of A, you will get 2. It might seem complicated but if you observe properly, you will get the answer in a moment. You should get 2 so the pi should get cancelled. You see there are two options, (A) and (D), in which the term \((4 - \pi)\) is in the denominator and A is in the numerator. You see that when you put this value of A in (D), you get 2.
Answer (D)
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Karishma
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