[tex]\text{In the given triangle we can see that the two sides length is 2.7 ft}\\
\text{and 3.4 ft and the angle between them is }40^{\circ}\\
\\
\text{we know that the area of a triangle with given two sides a and b and }\\
\text{the angle between them, C is given by}\\
\\
\text{Area}=\frac{1}{2}ab\sin C\\
\\
\text{so using this formula, the area of the given triangle is}\\
\\
\text{Area}=\frac{1}{2}(2.7)(3.4)\sin(40^{\circ})[/tex]
[tex]\Rightarrow \text{Area}=\frac{9.18}{2}\sin(40^{\circ})\\
\\
\Rightarrow \text{Area}=4.59\sin(40^{\circ})\\
\\
\Rightarrow \text{Area}\approx 2.95[/tex]
Hence the area of the triangle is approximately 2.95 square feet
