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It depends.

For simple shapes there may be formulae which link the lengths of sides, measures of angles and other properties of the shape that enable you to calculate the distance.

In 3-dimensional Euclidean space, if the point A has coordinates (u,v,w) and B has coordinates(x,y,z), then the distance AB is

sqrt[(x - u)2 + (y - v)2 + (z - w)2]

The formula has a similar form in 2 dimension.

But distance need not be defined in this fashion - there are other valid metrics. One of them is the Taxicab geometry developed by Minkowski and based on a rectangular grid of roads as in Manhattan. For more on Taxicab geometry, follow the link.

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Q: How do you find distance in geometry?
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