How to get geodetic area? rgeos::gArea doesn't seem to work. Or area-preserving proje

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I need to get an area of different polygons at continental scale (like third of Africa etc.). Usual functions like rgeos::gArea work only in the projection units.

  1. Is there any function which works correctly in real square meters on the geoid surface? I.e. real, geodetic area?
  2. If not, what projection should I use to get the least distortion? I need to measure 6 really huge areas (like third of Africa), so UTM or national projections are out of question. Can I use a single one projection that has minimal distortion area-wise across the whole Africa? Right now I am thinking of Mercator projection used by google maps (EPSG:3857), but I am not really sure...

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