#### Answer

$1$ sq. unit

#### Work Step by Step

We first use the formula $A=\frac{1}{2}bh$ to find the area of the triangle:
$A=\frac{1}{2}bh$
$A=\frac{1}{2}(1)(2)$
$A=\frac{2}{2}$
$A=1$
Now, we use the formula $Area=\frac{1}{2}ab \sin C$ to verify the result:
$Area=\frac{1}{2}ab \sin C$
$Area=\frac{1}{2}(\sqrt 2)(2) \sin 45$
$Area=\frac{2\sqrt 2}{2} \sin 45$
$Area=\sqrt 2(\sin45)$
$Area=\sqrt 2(\frac{\sqrt 2}{2})$
$Area=\frac{\sqrt 2\times\sqrt 2}{2}$
$Area=\frac{2}{2}$
$Area=1$
Therefore, both the formulas give the same area which is $1$ sq. unit.