**THE METHODS OF CALCULATION OF ELLIPSOIDAL POLYGONS AREAS
BASED ON SOME MAP PROJECTIONS PROPERTIES**

P. Pedzich, J. Balcerzak

*Warsaw University of Technology, Department of Geodesy and
Cartography, Institute of Photogrammetry and Cartography*

*p.pedzich@gik.pw.edu.pl*

Calculation of ellipsoidal polygons is very important problem in geodesy and cartography.

There are known some methods of area calculation of geodetic polygons but they are limited to small figures.

The paper presents some new
methods of calculation areas of geodetic polygons which use some basic
properties of map projection especially locale scale.

There are presented 4
methods. The first one is based on approximation of polygon by elementary
trapezoids limited by parallels and meridians. The second method uses
approximation of ellipsoidal polygon by elementary spherical triangles. In the
third method there is employed equal-area projection of ellipsoid onto sphere.
The forth method uses equal-area projection of ellipsoid into plane. In the end
there is presented reduction of area located between curved image of geodetic
line and its chord.

Moreover paper presents comparison of these methods and its application to calculation areas of administration districts in Poland.