How can i calculate the area of a polygon in c++ only by knowing the x and y coordonates of the points which make the polygon?
A simple google search shows the answer provided that you are dealing with non-self-intersecting polygons. The sign of the area is positive if the points on the polygon are arranged in counterclockwise order. This formula does not assume that the polygon is convex.
http://mathworld.wolfram.com/PolygonArea.html
Here, the area is found by summing the determinent of neighboring points. Each determinent computes the area of the parallelogram formed by the vector e.g. (x1,y1) and (x2,y2) (where both vectors stem from the origin (0,0)). The division by 2 gives the area of a triangle. When traveling around the polygon, the triangles will have a positive area if your polygon is convex. Otherwise, negative areas of these triangles will cancel with their positive counterparts for the case of a concave polygon giving you the correct result.