Godot

You mentioned the areas being countries. This leads me to believe that they are concave figures, correct? If you are unfamiliar, a concave figure is something that has a space that doubles back into the interior of the shape. So an o is convex, and a c is concave, as an example. Convex shapes are much simpler to find the area of. You can use a Riemann Sum as others have suggested. I would probably just pick a point inside the shape and do a bunch of triangles around with the point as an apex and the bases as two points on the edge of the surface, then sum up the areas of each triangle. You could even probably use a triangulation algorithm built into the engine to do this. (I am unfamiliar with the specifics of the Godot engine).

For concave shapes it becomes a little more complex. It has been mentioned that you can draw a bounding box around the shape, so that would allow you to calculate it using a numerical method. Take random samples inside the bounding box and count up the number that are inside the shape and divide by the total number of samples. The value you get will be the % of the area of the bounding rectangle that the shape takes up, so just multiply the easy area by the % and you will get an answer that is close enough. It may take a bit to get the sample count right, but it will get there. Try to make sure the samples are as uniform as possible. You could even scatter the sample points then relax them for a couple iterations before counting to increase accuracy without increasing samples.