The polygon can be represented by points on a graph which are the vertices of the polygon. So for polygon with n sides we will have n vertices. We represent the coordinates of the vertices by (xi,yi) where 1≤i≤n.
Graphing the points enables us to see in which order we need to add n determinants. Starting at any vertex we move from vertex to vertex anticlockwise. This determines which coordinates are (x1,y1), (x2,y2), ..., (xn,yn). The area A of the polygon is given by half the sum of the determinants:
⎜xi xi+1⎟
⎜yi yi+1⎟
If we call this determinant Di, then A=½(D1+D2+...+Dn-1).