Question 1149554
What is the area of the rectangle? Show all work.

Coordinates: A(-4, 0), B(-6, 4), C(4, 4), D(2, 8)
----------
Here's a method for any polygon, and # of sides:
----
<PRE>

 A    B    C    D    A
-4   -6    4    2   -4
 0    4    4    8    0

</pre>

Add the diagonal products starting at the upper left:
-4*4 + -6*4 + 4*8 + 2*0 = -16 - 24 + 32 + 0 = 8
---
Add the diagonal products starting at the lower left:
0*-6 + 4*4 + 4*2 + 8*-4 = 16 + 8 -32 = -8
---
The difference is 16
The area is 1/2 that, = 8 sq units.
-----------------------
The points have to be in order around the polygon, the only restriction.
==================
The points are not in order, so the area is not 8 sq units.
You can list them in order, then do the calculations.
---------------
It seems to work for polygons of all shapes, not just convex polygons, but I'm not yet certain of that.
=========================
Update:  it works for all "simple polygons."  Which means the vertices are listed in order.
---
Ref:  CRC Press, 32nd Edition