Question 1071016
<pre><b><font size=5>
To find out what order to taken the vertices, we plot
the parallelogram:

{{{drawing(12800/27,400,-1.9,8.9,-1.9,10.9,

graph(12800/27,400,-1.9,8.9,-1.9,10.9),line(0,0,3,3),
line(3,3,7,9), line(7,9,4,6), line(4,6,0,0),

locate(0,0,"(0,0)"),
locate(3,3,"(3,3)"),
locate(7,9,"(7,9)"),
locate(3,6.5,"(4,6)")  )}}}


To get the positive value of the area, take the coordinates 
going counter-clockwise around the polygon. Put the first
pair of coordinate (0,0) again at the bottom:

{{{matrix(1,3,

Area,
""="",
expr(1/2)abs(matrix(5,2,

0,0,3,3,7,9,4,6,0,0))))}}}

To evaluate that determinant, add all the NW to SE diagonal
products and subtract all the NE to SW diagonal products.

(0×3)+(3×9)+(7×6)+(4×0)-(0×3)-(3×7)-(9×4)-(6×0) =

  0  +  27 +  42 +   0 -   0 -  21 -  36 -   0  =

 12.  

Multiply by {{{1/2}}}:

So {{{matrix(1,5,

Area,
""="",
expr(1/2)12,
""="",
6)}}}

Edwin</pre></b></font>