What many flat earthers in these comments seem to be doing is failing to differentiate between a projection of a spherical earth onto a flat 2 dimensional surface and A FLAT 2 DIMENSIONAL SURFACE! The flat earth map would be a map of a flat 2 dimensional surface, whereas the mercator projection would be a projection of the 3d spherical earth onto a flat 2 dimensional surface.

Take the Flat Earth Map on the FE wiki. It is literally an azimuthal equidistant projection of the 3d spherical earth. It is the map that the UN uses for their logo, and flat earthers seemed to have taken it for their own. If you interpret this map as being a projection of the 3d spherical earth (an azimuthal equidistant one), then you realize that the areas further away from the north pole are increasingly distorted in size and shape, and then if you try to calculate quantities such as surface areas of countries you can correct for this distortion mathematically and arrive at the correct answer that we observe in reality.

If however you treat this map as an actual literal map of a flat earth (that is, an x to 1 linear projection of the flat earth, where x is the scale factor which linearly relates distances on your map to distances on the flat earth such that 1 unit of length on your map corresponds to X units of length on the flat earth), then if you try to go and calculate surface areas of countries you have no reason to try to correct for distortion, since there is no distortion in a one to one map, a special feature of a map of a flat surface. You will therefore find that your answers are totally off.

I find it sort of funny that flat earthers use a literal projection of the spherical earth as their map, one used by the UN on their logo no doubt.