Math to calculate area of polygon
by ericlin

This discussion is a note after reading the page:

http://www.brunel.ac.uk/~castjjg/java/polygon/polygon.html

The most wonderful thing in that page is the idea that the calculated area of a triangle can be "signed". Positive means clockwise and Negative means counterClockwise. So, the equation to calculate the area of polygon is very very simple.

To calculate the area of a polygon composed by pt0,pt1,pt2,pt3,pt34,pt5 the equation is like this:

area=function(ptA,ptB){
    return (ptA.x*ptB.y-ptA.y*ptB.x)/2;
}
polygonArea=area(pt0,pt1)+area(pt1,pt2)+area(pt2,pt3)+area(pt3,pt4)+area(pt4,pt5)+area(pt5,pt0);

It is just a function sum of sequential points. Of-course, we are talking about a closed polygon. 

At the last few lines of that page, the professor did not try to explain the details to convince me that equation is valid. He gave only two examples which is not enough for me.

So, I try to convice myself. Here is my notes.

First lets try to calculate the area of an arbituray triangle.

You see, if we make C to be (0,0), then for a vector A->B, the triangle area will be just 

area=(A.x*B.y-A.y*B.x)/2;

Lets try another way to calculate the area of an arbituray triangle by that equation:

Lets add a corner to the side of A->B, so the triangle will be quandrangle.