Question 1154317
<pre>
{{{drawing(400,1000/3,-5,7,-5,5,
line(-4,2,3,-4),line(3,-4,6,2),line(6,2,1,4),line(1,4,-4,2),
graph(400,1000/3,-5,7,-5,5),
circle(-4,2,.1),circle(3,-4,.1),circle(6,2,.1),circle(1,4,.1) )}}}

Since the polygon is convex (has no "sunk-in" places), we make this
determinant of coordinates of vertices, repeating the first one at
the bottom. [It doesn't matter which vertex we start with].

{{{A=abs(
matrix(5,2,

 -4, 2, 3, -4, 6, 2, 1, 4,-4,2))}}}

We multiply and add all the "northwest to southeast"-diagonals:

(-4)(-4)+(3)(2)+(6)(4)+(1)(2) = 16+6+24+2=48


We multiply and add all the "northeast to southwest"-diagonals:

(2)(3)+(-4)(6)+(2)(1)+(4)(-4) = 6-24+2-16=-32

Subtract: 48-(-32) = 48+32 = 80

Do the other one the same way.  Graph it to make sure it is
a convex polygon.  [If the polygon is concave, we would break it 
into convex polygons]. If the area comes out negative, just take
the absolute value, making it positive.

Edwin</pre>