Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The area of the shaded region in the adjoining figure is $a^{2}(\pi-1)$ sq. units
(b)$a^{2}\left(\frac{\pi}{2}-1\right)$ sq. units
(c)$\frac{a^{2}}{2}(\pi-1)$ sq. units
(d)$\frac{a^{2}}{2}\left(\frac{\pi}{2}-1\right)$ sq. units
Answer
Answer (as printed): B
Explanation
Area of the shaded region = Area of the semi-circle with radius $a$ units - Area of the triangle with base $2 a$ units and height $a$ units $$\begin{aligned} & =\left(\frac{\pi a^{2}}{2}-\frac{1}{2} \times 2 a \times a\right) \text { sq. units. } \\ & =\left(\frac{\pi a^{2}}{2}-a^{2}\right) \text { sq. units }=a^{2}\left(\frac{\pi}{2}-1\right) \text { sq.units } \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.