Answer
$$\sqrt 6$$
Work Step by Step
We have $ r_u=1+j \space and \\ r_v=1-j+k $
and $$|r_u \times r_v|=\sqrt 6$$
$$ Surface \space Area=\iint_S |r_u \times r_v| \space du \space dv \\=\int_0^1 \int_0^1 \sqrt 6 \space du \space dv \\=\sqrt 6(1-0) \\=\sqrt 6$$
