If we have a constant slope, we can use the QTO feature in Civil 3D to assign the appropriate pay item to the desired link(s). Then use the Takeoff to get the area. This should result in a plan area. To get the slope area we can multiply it by a slope ratio. For example, if the slope is 2:1 we can multiply it by 1.1803398749895 to get the slope area.
If the slope isn't constant it gets harder. One option is to run the slope stake report and then calculate the slope length of the link and then use the average link length to get the area.
Another option is to create boundaries around the slope areas we want and use the surface properties to get the slope area.