Area of Convex polyhedron (2D) with unordered vertices

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I am aware that an algorithm exist to find area of a convex polyhedron when the vertices are given in order. But, I have a convex polyhedra which does not have vertices in order and I wish to compute its area.

I thought of 2 possible approaches -

  • Convert the unordered vertices into ordered vertices (Can it be done using Convex Hull of the polytope?)
  • A direct algorithm which computes area using the unordered vertices

An answer using any one of the above mentioned approaches will satisfy my question.

PS - Mentioning any avaialble packages (in C) which will solve my problem will be a plus.