Answer
$$1{\text{ sq unit}}$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle we have:}} \cr
& C = {45^ \circ } \cr
& b = 2\,\,\,\,\,h = 1 \cr
& {\text{Find the area of the triangle using the formula }}A = \frac{1}{2}bh \cr
& Area = \frac{1}{2}\left( 2 \right)\left( 1 \right) \cr
& Area = 1{\text{ sq unit}} \cr
& {\text{Find the area of the triangle using the formula }}A = \frac{1}{2}ab\sin C \cr
& {\text{With }}b = \sqrt 2 {\text{ and }}a = 2 \cr
& Area = \frac{1}{2}\left( 2 \right)\left( {\sqrt 2 } \right)\sin \left( {{{45}^ \circ }} \right) \cr
& Area = \left( {\sqrt 2 } \right)\left( {\frac{{\sqrt 2 }}{2}} \right) \cr
& Area = 1{\text{ sq unit}} \cr
& {\text{Both results are the same}} \cr} $$
