ABC26GN4603 · Area
Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If $M N=x$, then what is the area of the shaded region? $\pi x^{2}$
(b)$\frac{\pi x^{2}}{2}$
(c)$\frac{\pi x^{2}}{2}$
(d)$\frac{\pi x^{2}}{4}$
Answer
Explanation
Area of the shaded region $$\begin{aligned} & =\frac{1}{2} \pi\left(\frac{L M}{2}\right)^{2}+\frac{1}{2} \pi\left(\frac{L N}{2}\right)^{2}+\frac{1}{2} \pi\left(\frac{M N}{2}\right)^{2} \\ & =\frac{1}{8} \pi\left[(L M)^{2}+(L N)^{2}+(M N)^{2}\right]=\frac{1}{8} \pi\left[2(M N)^{2}\right] \\ & =\frac{1}{4} \pi(M N)^{2}=\frac{1}{4} \pi x^{2} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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