Graph the points:



Get them in order going counter-clockwise around
the polygon.  

(-2,3), (4,0), (8,7) (5,10), and (1,10).

Now we write the equation for the area in terms
of the 6x2 "determinant" where each ordered pair of 
coordinates appear on each row in that counter-
clockwise order, repeating the first ordered pair 
of coordinates at the bottom.



Now to evaluate that "determinant" we 

Add the sum of the products of each x-coordinate 
by the y-coordinate of the point just below it,
and then subtract the sum of the products of each 
y-coordinate by the x-coordinate of the point just 
below it.

So we get

 









Edwin