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Adding faces to a mesh

I am trying to create a mesh (.stl file) that follows a bezier curve. I have succesfully created the side face but I have trouble creating the top and bottom faces. The problem is that the bezier curve is quite complex (the shape can be concave or convex) and the faces i have managed to create don’t follow the curve exactly (I will add a picture). Is there a way to make the top and bottom faces follow the curve exactly and also fill the shape (i don’t want it to be hollow).