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