Calculate the surface area of a simple (non-self-intersecting) n sides polygonal shape with known Cartesian coordinates in the plane for all of its vertices. The main concept of the method is to divide the main polygon in n trapezoids and to cross-multiply corresponding coordinates to find the area enclosing the polygon (green trapezoids), and subtract from it the surrounding trapezoids (red) to find the area of the polygon within. It is also called the shoelace formula because of the constant cross-multiplying for the coordinates making up the polygon, like tying shoelaces. Mainly applicable in topography.
Determine the coordinates of an unknown station P from three (3) previously coordinated reference points A, B and C visible from station P, only by measuring the angles subtended by lines of sight from station P to the three coordinated points. Resection technique is commonly implemented when the existing reference points are not accessible during a survey.