What surface's area is used to compute area of country? [closed]

Premise:

Earth's surface geometry is modelled by means of different geoids -depending on the objectives. The roughest and most basic are ellipsoids surfaces. Yet, on a small scale, e.g., area of private parcels of farmer's land, municipalities areas - direct measurements, local geometry and neglecting any curvature are used to compute areas. At this scale, 100 m by 100 m parcel does have an area of 10'000 sqm - even if it lays on a slope 45° inclined.

Problem

If we increase the scale and consider a country like Switzerland - in which a good part of the territory is made up of slopes, it is not clear to me how is the country area calculated. In other words:

1. Is the area obtained by a bottom up approach - summing up the small areas of the small parcels of territory? in which case the overall area accounts for the effective, real, extension of the land …
2. Is the area calculated by calculating the area of a simplified country surface which is NOT the union of all the small parcels? in which case the country area is NOT equal to the sum of the areas of the small parts …
3. If 2 is the case, does the simplified country surface still include slopes or is it made "flat" (slope's area is the area of the projection on the base)?
4. ACID Test: if a country includes great many low inclined slopes would its area change if the slopes were flattened?

closed as too broad by PolyGeo♦Sep 18 '18 at 22:58

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Welcome to GIS SE! As a new user be sure to take the Tour where you will see that there should be only one question asked per question under our focussed Q&A format. – PolyGeo Sep 18 '18 at 22:58
• Where is the country area that you are investigating being reported? In other words, can you link to a value for Switzerland's area so that it specifically can be investigated? If there are multiple areas reported by multiple people then there may be MANY answers for how particular people have decided to calculate it. – PolyGeo Sep 19 '18 at 0:01
• Triangulation reduces the error. see math.stackexchange.com/questions/404468/… – Mapperz Sep 19 '18 at 1:19