Answer
$8$ square feet
Work Step by Step
The area of a triangle is half the product of the lengths of two sides multiplied by the sine of the included angle.
$\text{Area}=\frac{1}{2}bc\sin A=\frac{1}{2}ab\sin C=\frac{1}{2}ac\sin B$
The area of the triangle is calculated as below:
$\begin{align}
& \frac{1}{2}ab\sin C=\frac{1}{2}\left( 4 \right)\left( 6 \right)\sin 42{}^\circ \\
& =12\sin 42{}^\circ
\end{align}$
Using a calculator we get
$12\sin 42{}^\circ \approx 8$
So, the area of the triangle is approximately $8$ square feet.
