In geometry a flat surface is usually called a plane surface, or just a plane. You use it like this.
1) If straight lines lie in the same plane they a said to be co-planar.
2) If two co-planar straight lines never intersect, they are parallel to each other.
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A mirror with a flat surface - planar
Its base is a flat surface
A flat surface generally refers to a horizontal surface and is referred to as the plane.
A flat surface is no more that a plain horizontal surface with no depth. For example the surface of a table top is a flat surface, that is the surface only, not the depth of the top or the rest of the table
A flat surface that extends forever is a plane