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Have a look at my reply to this topic. I think your formula is based on that idea, just simplified a lot.
I was given this formula
For any regular polygon;
If you only need to solve one (or a few), then break into triangles as irspow suggested. But there are methods to do it automatically using a conmputer algorithm.
The perimeter would simply be the sum of the lengths of all sides. To get the area you either need to break down the irregular polygon into regular polygons and sum their areas or integrate the equations that describe the upper and lower bounderies of the shape in question.
How do you calculate the the area and perimeter of an irregular polygon knowing the length of sides