#### Answer

The area of the triangle is 10 square feet.

#### Work Step by Step

The area of the triangle is half the product of the lengths of the two sides multiplied with sine of the included angle.
In the given problem, the given data is $C=36{}^\circ,\ a=5\ \text{feet, and }b=\text{7}\ \text{feet}$.
Therefore, the required area is
$\begin{align}
& \text{Area}=\frac{1}{2}\left( 5 \right)\left( 7 \right)\left( \sin \,36{}^\circ \right) \\
& =\frac{1}{2}\left( 5 \right)\left( 7 \right)\times 0.89100 \\
& =10
\end{align}$
Therefore, the required area is 10 square feet.