In geometry we are taught to find the area of a shape by a given formula. For example, the trapezoid shown in the figure has a formula for area of
A = 1/2 *((base 1 + base 2)/2)*height
But for polygons drawn on a Cartesian plane with known coordinates, the formula for area is
A = 1/2 * determinant
The determinant refers to the determinant of the matrix of coordinates. It is a two-column matrix, wherein the first column is the x-coordinate and the second is the y-coordinate. Just make sure that the points are arranged such that they are adjacent with each other. The matrix for this would be
-5 -2 <---- point A
-1 2 <---- point B
0 -1 <---- point C
-2 -3 <---- point D
-5 -2 <---- point A
Just cross multiply the coordinate with a pattern shown in the picture. Don't mind the numbers. Focus on the pattern for determining the matrix. In this case,
Area = 1/2 * [(-10-2)+(1-0)+(0-2)+(4-15)]
Area = 12 square units