A plane horizontal surface with no depth refers to a flat area on a curved surface.
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Surface
A cuboid has 6 flat faces but no curved surfaces. ..________ ./............../| /_______/.| |..............|.| |..............|./ |_______|/
It is called the surface area.
When information is moved from a curved surface( like the Earth) to a flat surface ( like a map), distortion occurs.
Normally a cube has 6 flat surface faces