If all you will do is extrude it, thus extend it in the perpendicular direction, then you should not do so. Instead, reduce the problem, since all derivatives in that cross direction should be zero. (Look for the terms plane stress and plane strain. You should have learned about them in your studies.) This is a common practice in engineering, thus converting a 3-dimensional problem to a problem in only 2 dimensions.
Is that correct here? Probably not, since you don't really want to simply extrude it in that direction, but make a profile that will change with Z, thus the third dimension.
