RRB NTPC Mains or Stage 2 Model Paper 4 with solutions

(a) In DABC,

BC $=\sqrt{{\mathit{x}}^2+{\mathit{y}}^2}$
∴ Area of ΔABC$=\frac{1}{2}\times \mathit{x}\times \mathit{y}=\frac{1}{2}\mathit{x}\mathit{y}$
Area of semi-circle BACB $=\frac{\mathit{\pi }\left({\mathit{x}}^2+{\mathit{y}}^2\right)}{4}$
∴Area of shaded portion = Semi-circle ABDA + Area of semi-circle AECA – (Area of semi-circle BACB – Areaof ΔABC)
$=\frac{\mathit{\pi }{\mathit{x}}^2}{4}+\frac{\mathit{\pi }{\mathit{y}}^2}{4}-\mathit{\pi }\left[\frac{\mathit{x}+{\mathit{y}}^2}{4}\right]+$ Area of ΔABC
= Area of ΔABC