section_path: Area formulas/Polygon formulas
section_name: Polygon formulas
paragraph_text: Polygon formulas
  
  For a non-self-intersecting (simple) polygon, the Cartesian coordinates (x i, y i) {\displaystyle (x_{i},y_{i})} (i =0, 1,..., n -1) of whose n vertices are known, the area is given by the surveyor's formula:
  
  where when i = n -1, then i +1 is expressed as modulus n and so refers to 0.