Calculate Earth convex hull polygon area given latitude and longitude

Question

I have searched for explanations and algorhitms how to calculate Earth\'s polygon surface area. I\'ve found this and this
Lets say I got already convex hull points
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Answer 1

The algorithm for finding the area of a polygon on a sphere can be found here:
Thread: A method to compute the area of a spherical polygon

You could also use this NASA JPL paper for some algorithms:

Some algorithms for polygons on a sphere.