I appendix the R script and a minimum convex polygon i made

Hi, you can use the polyarea function of MATLAB for example.

• Pick a certain base point（the given or unknown free point ， in the boudary of the polygon） in the convex area ，sequently connect the vertexes to the reference point clockwisely, the polygon is segmented into multiple decreted trangles。 Apply the determinant formula of the trigon area in the Cartesian coordinates to calcute the area of each single trangle ，then sum up all the items to the final result 。
• Also，You can apply some other segmentation solutions to calculate .