How do topographers measure the surface area of countries given the coastline paradox?

As I understand it, the coastline paradox states that it is impossible to 100% accurately measure a coastline, since you can always 'zoom-in' more, down to the atomic level, and thus the length would become infinitely long.

Wouldn't this principle apply to measuring the surface area of a country? Land isn't flat - it has bumps and dips (mountains and valleys) that vastly increase its true surface area, but you can also continue to 'zoom-in' to every rock and grain of sand until the surface area becomes infinitely large. Given this, how do topographers measure the land area of countries? Do they simply assume all countries are uniformly flat, and thus measure the area based on the approximate lengths of the borders, or do they take into account the fact that terrain is not flat? If the latter is true, at what point do they stop 'zooming-in'?