Given,
The measure of the sides is 12 and 20 sqrt(2).
The measure of the including angle is 45 degree.
Required
The area of the triangle.
The area of the triangle is calculated as,
[tex]\begin{gathered} Area=side1\times side2\times\frac{sine\text{ of }angle}{2} \\ Area=20\sqrt{2}\times12\times\frac{sin45^{\circ}}{2} \\ Area=20\sqrt{2}\times12\times\frac{1}{2\sqrt{2}} \\ Area=20\times6 \\ Area=120 \end{gathered}[/tex]Hence, the area of the triangle is 120 unit^2.