Area of the region defined by $1\le \left|\mathrm{x}\right|+\left|\mathrm{y}\right|$ and ${\mathrm{x}}^2-2\mathrm{x}+1\le 1-{\mathrm{y}}^2$ is $\mathrm{k\pi }$ then k =

${\mathrm{x}}^2-2\mathrm{x}+1\le 1-{\mathrm{y}}^2$

$\Rightarrow {\left(x-1\right)}^2+y^2\le 1$

Represents a circle with centre (1,0)

Required area = area of circle- area of sector ABC=$\mathrm{\pi }{\left(1\right)}^2-\frac{1}{2}{\left(1\right)}^2\frac{\mathrm{\pi }}{2}=\mathrm{\pi }-\frac{\mathrm{\pi }}{4}=\frac{3\mathrm{\pi }}{4}$

$k\mathrm{\pi }=\frac{3\mathrm{\pi }}{4}\Rightarrow \mathrm{k}=\frac{3}{4}$