Is it possible to calculate the surface area of the top (table & crown) of a round diamond using the GIA certificate report?

Do you mean the surface area of all of the facets or the visual size given by the diameter?

To calculate the surface area you’d need the dimensions of the table, star facets, bezel facets, and upper girdle facets. That information is not available on the GIA report. You could approximate it as part of a cone given the crown angle, but you’ll need to break out your calculus integrals to do it since the standard cone surface area cone assumes a full cone (like the pavilion).

If you’re just interested in the visual size, then the standard formula for the area of a circle based on the diameter of the diamond would work.

That’s the length x width x depth. The average diameter of the diamond would be (length + width)/2 or 6.84mm in this case.

What do the “Measurements” in the GIA certificate report represent?

see image below for what I am referring to,

https://imgur.com/JoUM4iu