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I think it will work, the displacement method. Try it theoretically, put a 10cm cube into a full container of water completely submerged, it'll displace it's exact volume in water. That water should now have the same surface area (the water displaced) as the original cube as both are effectively incompressable. Just put the displaced water in a container you can measure and complete the maths on.It'll even do a the little rimple dimple detail for you.
I’m not sure that would work, as displacement is related to volume and not surface area. You could work out cubic centimetres by this method but not square centimetres. Two objects can have the same volume but different surface areas.
Or, "The density of steel is in the range of 7.75 and 8.05 g/cm3 (7750 and 8050 kg/m3 or 0.280 and 0.291 lb/in3). The theoretical density of mild steel (low-carbon steel) is about 7.87 g/cm3 (0.284 lb/in3). Density of carbon steels, alloy steels, tool steels and stainless steels are shown below in g/cm3, kg/m3 and lb/in3."From this site https://amesweb.info/Materials/Density_of_Steel.aspx which would mean, if you weigh the components, each 7.87 gram would occupy a cubic centimeter, which gives the maths route to calculate total surface area for plating. Which looks to me that you can reliably give a surface area for the components as mass of the low carbon steel is a constant. Is that true ?