#### Answer

$356$ cm$^{2}$

#### Work Step by Step

The area of the triangle is half the product of the length of two sides and the sine of the angle included between them:
$Area=\frac{1}{2}ac \sin B$
We substitute the values of $a,B$ and $c$ in this formula and solve:
$Area=\frac{1}{2}ac \sin B$
$Area=\frac{1}{2}(30.4)(28.4) \sin 124.5^{\circ}$
$Area=\frac{1}{2}(863.36) \sin 124.5^{\circ}$
$Area=431.68 \sin 124.5^{\circ}$
Using a calculator, $\sin 124.5^{\circ}=0.8241$. Therefore,
$Area=431.68 \sin 124.5^{\circ}$
$Area=431.68(0.8241)$
$Area=355.75\approx356$
Therefore, the area of the triangle is $356$ cm$^{2}$.