A painter is going to apply a special coating to a triangular metal plate on a new building. Two sides measure $16\mathrm{.}8$ cm and $13\mathrm{.}4$ cm $.$ She knows that the angle between the two sides is $113.$ What is the area of the surface she plans to cover with the coating?

The surface area is $c{m}^2.$

$($Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.$)$