Geometrical properties of arbitrary sections (2D)

[cigarette]

Hi all, i am interested in finding out the Geometrical properties of an arbitrary section, which means 2D area. Rather than having to perform manual calculations everytime, i am trying to write a program to help me with this. There is a problem however. I cannot seem to find the appropriate mathematical expressions to help me obtain the following :

(1) Area
(2) Centroid
(3) Moment of Inertia

To help make the program easier to write, i have decided that all lines drawn are straight lines, therefore eliminating the tedious curves. Hence i can easily calculate the length of each lines and sum them up to obtain the perimeter. This is possible, because i have all the co-ordinate points. Now, what about area? I have tried using the Green's Theorem for calculations, but i am not sure whether it works for sections which have a large number of co-ordinate points. Also the centroid can also be worked out using Green's Theorem, and once again, it is not known whether it works for arbitrary co-ordinates. Does it have any limitations?

Can anyone help explain to me whether Green's Theorem is good for this application? Or does anyone have a clearer or better algorithm which i can use?

Thanks in advance ... it's rather urgent..

 

[HallsofIvy]

This same question was asked in "General Mathematics". Please do not post the same question multiple times.

 

[Feynman]

Green th is using on partial differentials eq , for the variational formulation than for finite element