Answer
${\rm{Area}}\left( S \right) \approx 20$
Work Step by Step
From the domain $0 \le u,v \le 2$ we get ${\cal R} = 2 \times 2 = 4$.
By Eq. (3):
${\rm{Area}}\left( S \right) \approx ||{\bf{N}}||{\rm{Area}}\left( {\cal R} \right) = 5 \times 4 = 20$
