It looks like this is not as exciting as the Monte Carlo method.
You will need the criteria for each point (X,Y) coordinate against each of your lines in your example.

It looks like the top line is Y<275000, bottom line is Y > 122500, left bottom line is Y < -6000X + 280000, etc. You would get the equation for each ine and then determine if it is < or > by tossing in point (0,0) and see which symbol works.

Then generate your points and if it passed the test for each line (it looks like there is 7 of them), then it is inside your figure.

If you need the area inside your figure it is a real easy formula if you have the coordinates of each vertex.