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.
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:
- 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 …
- 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 …
- 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)?
- ACID Test: if a country includes great many low inclined slopes would its area change if the slopes were flattened?