Question 268147
<pre><font size = 4 color = "indigo"><b>
Graph the points:

{{{drawing(400,400,-3,9,-1,11,
locate(-3,2.6,"(-2,3)"),
locate(1,10.5,"(1,10)"), 
locate(5,10.5,"(5,10)"),
locate(8,7,"(8,7)"),
locate(4.5,.5,"(4,0)"),

graph(400,400,-3,9,-1,11),

line(-2,3,1,10),

line(1,10,5,10), 

line(5,10,8,7),

line(8,7,4,0),

line(-2,3,4,0)  )}}}

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.

{{{A=(1/2)abs(matrix(6,2,

-2,3, 
4,0, 
8,7, 
5,10,
1,10,
-2,3))}}}

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

{{{A=(1/2)((-2)(0)+(4)(7)+(8)(10)+(5)(10)+(1)(3))-((3)(4)+(0)(8)+(7)(5)+(10)(1)+(10)(-2))}}} 

{{{A=(1/2)(0+28+80+50+3)-(12+0+35+10-20)}}}

{{{A=(1/2)(161-37)}}}

{{{A=(1/2)(124)}}}

{{{A=62}}}

Edwin</pre>