Yes, there it is. It is something that possesses only length (and not width or height)
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1d has only the length, but 2d has both the length and width.
It doesn't have any volume (3D) and it's not a line (1D). Thus, it is a 2D shape.
the distance between 2 points (a 1d line) is measured in milimetres. Square metres are used to measure area (a 2d shape). There isn't enough info to answer your question. Its like asking 'whats the area of a shape with an unknown number of sides, if i only have the length of one of the sides'.
In 3 dimensional graphing, a plane is a 2 dimensional solution to an equation. In other terms, a plane is all lines parallel to each other where one point on each line is colinear with one point on each line. Associate point:0d, line:1d, plane:2d.
A curved surface is like imagining a sheet of paper that is bent or a flag waving in the wind. A curved edge is like an elastic stick bent in one(C curve) or more points(S curve). The curved surface beeing 3 dimensional(3D) and the curved edge 2 dimensional(2D) unlike the simple surface and edge which are 2D respectively 1D.