Answer
$4$ 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:
$\begin{align}
& \frac{1}{2}bc\sin A=\frac{1}{2}\left( 4 \right)\left( 5 \right)\sin 22{}^\circ \\
& =10\sin 22{}^\circ
\end{align}$
Using a calculator we get
$10\sin 22{}^\circ \approx 4$
So, the area of the triangle is approximately $4$ square feet.
