A room in the shape of a triangle has sides of length 6yd, 8 yd, and 13 yd. If carpeting costs $13.50/square yard, and padding costs $3.25/square yard, how much to the nearest dollar will it cost to carpet the room?

You can compute area using Heron's formula
Area=\frac{1}{4}\sqrt{(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)}
where a,b,c, are sides of the triangle.
Then multiply the cost of carpet. Similarly for padding.

"how much to the nearest dollar will it cost to carpet the room?"
means that if you get say $30.5, then "the nearest dollar" is $31, if you get $30.499, the nearest dollar is $30.