Calculate Earth convex hull polygon area given lat

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
[56.992666,24.126051], [58.00282,25.930147], [58.787955,25.565078], [59.4997,24.861427], [59.463678,24.711365], [59.395767,24.599837], [56.992666,24.126051]

From second link the first answers uses Python library and second answer approach won't give quite precise area even if we assume that Earth is sphere (am I right)? What approaches could I take for calculating the area (less expensive) if we assume that Earth is sphere?

In addition, I have looked for different libraries (geotools.org etc) but haven't found in their documentation about area calculation.

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.