Answer
${\rm{Area}}\left( S \right) \approx 0.0006$
Work Step by Step
We have ${\rm{Area}}\left( {\cal R} \right) = 0.01 \times 0.02 = 0.0002$ and ${{\bf{T}}_u} \times {{\bf{T}}_v} = \left( {1,2,2} \right)$ at a sample point in the rectangle. So,
$||{\bf{N}}|| = ||{{\bf{T}}_u} \times {{\bf{T}}_v}|| = \sqrt {1 + 4 + 4} = 3$
By Eq. (3):
${\rm{Area}}\left( S \right) \approx ||{\bf{N}}||{\rm{Area}}\left( {\cal R} \right) = 3 \times 0.0002 = 0.0006$
