Answer: $B.$ $2$
$x+y=1$. when$ x>0 $ and$ y>0$
$-x+y=1$ when $x<0$ and $y>40$
$-x-y=1$ when both $x$ and $y$ are $<0$
$x-y=1$ when $x>0$ and $y<0$
Now, on plotting these equations,
The obtained coordinates would be:
$(1,0) (0,1) (-1,0) (0,-1)$
On joining these co-ordinates, a square of side $\sqrt2$ units would be obtained.
Therefore, area enclosed $= $ Area of square $=(\sqrt2)^2 = 2$ units
Therefore, option $B$ is the right answer.