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

$$\begin{gathered} 1\le \left|x\right|+\left|y\right|\text{ represents the region outside } \\ \text{ the square and }{\mathrm{x}}^2-2\mathrm{x}+1\le 1-{\mathrm{y}}^2\text{ represents the region } \\ \text{ inside the circle, as shown in the figure. } \end{gathered}$$

$\text{ Area }={\mathrm{\pi r}}^2-\frac{1}{2}{\mathrm{r}}^2\mathrm{\theta }$=$=\pi -\frac{\pi }{4}=\frac{3\pi }{4}.=k\mathrm{\pi }\Rightarrow \mathrm{k}=3/4$