Refined algorithm for calculating area distortion adjustments of geospatial objects in geodetic projections

Area, as one of the fundamental geometric parameters of land parcels, is a key factor in land management, land cadaster, land taxation, and related fields. The geodetic area should ideally be determined on the surface of the reference ellipsoid; however, in engineering practice, it is usually calculated from the coordinates of turning points in the Gauss-Krüger projection. The influence of projection is approximately accounted for by introducing a correction to the computed area value derived from rectangular coordinates. At the same time, the geodetic area may differ significantly from its approximate value.