Question

The area enclosed by the curves $|y +x| \leq 1$, $|y-x| \leq 1$ and $2 x^{2}+2 y^{y}=1$ is

• A. $\left(2+\frac{\pi}{2}\right)$ sq units
• B. $\left(2-\frac{\pi}{2}\right)$ sq units
• C. $\left(3+\frac{\pi}{2}\right)$ sq units
• D. $\left(3-\frac{\pi}{4}\right)$ sq units

Answer 1

Answer: (B)

The curves $y+x \leq 1$ and $|y-x| \leq 1$ form a square $A B C D$ and $2 x^{2}+2 y^{2}=1$ is a circle of radius $\frac{1}{\sqrt{2}}$ and center $(0,0)$.

$\therefore $ Required Area
= Area of square - Area of circle
$=\left(2-\frac{\pi}{2}\right)$ sq units