Finding random x,y coordinates in a figure where you know the boundary

The goal is to find coordinates in a figure with an unknown shape. What IS known is a list of coordinates of the boundary of that figure, for example:

boundary = [(0,0),(1,0),(2,0),(3,0),(3,1),(3,2),(3,3),(2,3),(2,2),(1,2),(1,3),(0,3),(0,2),(0,1]

which would look something like this:

Square with a gab

This is a very basic example and i'd like to do it with very larg lists of very different kinds of figures.

The question is how to get a random coordinate that lies within the figure WITHOUT hardcoding the anything about the shape of the figure, because this will be unknown at the beginning? Is there a way to know for certain or is making an estimate the best option? How would I implement an estimate like that?