The perimeter of a figure is always the sum of the lengths of the sides.
If we have the coordinates of the vertices of the quadrilateral, we can calculate the length of each side as the distance between the vertices.
For example, the length of a side AB will be the distance between the points A and B:
[tex]d=\sqrt[]{(x_b-x_a)^2+\mleft(y_b-y_a\mright)^2}[/tex]Adding the length of the four sides will give the perimeter of the quadrilateral.
