Question 966654
find the area of the pentagon with vertices (3,0) (1,7) (5,3) (-4,2) (-3,-2)
<pre>
Plot the points so that we will know their counterclockwise order:

{{{drawing(2400/7,400,-6,7,-5,9, graph(2400/7,400,-6,7,-5,9),
line(1,7,-4,2),line(-4,2,-3,-2),line(-3,-2,3,0),line(3,0,5,3),line(5,3,1,7),
locate(-3.8,2,"(-4,2)"),
locate(-3,-2,"(-3,-2)"),
locate(1.5,.7,"(3,0)"),
locate(5,3,"(5,3)"),
locate(1,7.6,"(1,7)")


)}}}

1. List the coordinates in an array, repeating the first one
at the bottom of the list.

2. Add all the diagonal products that go from "northwest to southeast",
and subtract all the diagonal products that go from "northeast to 
southwest", like this:

{{{matrix(7,5,
   x,y, "","","",
   1,7, (1)(2)-(7)(-4),""="",2+28=30,
  -4,2, (-4)(-2)-(2)(-3),""="",8+6=14,
 -3,-2, (-3)(0)-(-2)(3),""="",0+6=6,
   3,0, (3)(3)-(0)(5),""="",9-0=9,
   5,3, (5)(7)-(3)(1),""="",35-3=32,
   1,7, "",            "",    "")}}}
 
Add all the numbers on the right:

30+14+6+9+32= 91

Divide by 2:

Answer: Area = 45.5

Edwin</pre>