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The arch of the top part was consistent so I just copied the arch and connected the dots.The corners bend 2 ways.
What you want is a splined surface. Professional CAD software (e.g. Solidworks) has built-in support for this. I'm guessing Sketchup may not?
I think they call that "hand stitching" in Sketchup. All 4 edges are different and if I just stitched them together it would be flat and not follow the curves.It would look something like this hot mess:I guess it will have to work since it will need a light sanding anyways.