  We compute the value of the $L^1$-relaxed area of the graph of the map $u :
B_l(0)\subset \mathbb R^2 \mapsto \mathbb R^2$, $u(x):= x/\vert x\vert$, $x
\neq 0$, for all values of $l>0$. Interestingly, for $l$ in a certain range, in
particular $l$ not too large, a Plateau-type problem, having as solution a sort
of catenoid constrained to contain a segment, has to be solved.
