Answer
$20.3$ ft$^{2}$
Work Step by Step
First, we convert decimal minutes to degrees:
$35^{\circ}10'=35\frac{10}{60}=35.17^{\circ}$
The area of the triangle is half the product of the length of two sides and the sine of the angle included between them:
$Area=\frac{1}{2}ab \sin C$
We substitute the values of $a,b$ and $C$ in this formula and solve:
$Area=\frac{1}{2}ab \sin C$
$Area=\frac{1}{2}(6.90)(10.2) \sin 35.17^{\circ}$
$Area=\frac{1}{2}(70.38) \sin 35.17^{\circ}$
$Area=35.19\sin 35.17^{\circ}$
Using a calculator, $\sin 35.17^{\circ}=0.57600$. Therefore,
$Area=35.19\sin 35.17^{\circ}$
$Area=35.19(0.57600)$
$Area=20.27$
Therefore, the area of the triangle is $20.3$ ft$^{2}$.