If the distance of any point (x, y) from origin is defined as $\mathrm{d}(\mathrm{x},\mathrm{y})=\left|\mathrm{x}\right|+\left|\mathrm{y}\right|$  , then the locus $\mathrm{d}(\mathrm{x},\mathrm{y})=1$  is a

$\mathrm{d}(\mathrm{x},\mathrm{y})=1\Rightarrow \left|\mathrm{x}\right|+\left|\mathrm{y}\right|=1$
The graph of which is shown in the figure

The graph is a square  $\mathrm{AB}=\mathrm{BC}=\mathrm{CD}=\mathrm{DA}=\sqrt{2}$
Where,  $\mathrm{OA}=1=\mathrm{OB},\angle \mathrm{ABC}={90}^0$
$\therefore \mathrm{Area}=\mathrm{AB}.\mathrm{AD}=\sqrt{2}\times \sqrt{2}=2\mathrm{sq}\mathrm{unit}$ .