There are several different metrics. The most common is the Euclidean or Pythagorean distance where if P = (a, b) and Q = (c, d) are two points in the Cartesian plane then the distance between then is sqrt[(a - c)^2 + (b - d)^2)]. Another metric is the Minkovski or taxicab measure, based on a grid structure of roads. Since you cannot travel "cross country", the distance would be |a - c|+ |b - d|.
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velocity
Since speed is a ratio between distance and the time it took to move that distance, the two required measures are Distanceand Time.
The perimeter
Yes the thickness of something is just a distance.
Mile