Thread: Centroid of a irregular polygon???????

Known the vertices of an IRREGULAR polygon (x1,y1), (x2,y2), (x3,y3)...... and so on how to find its centroid?

I tried to divide the polygon into differrent triangles with a common vertex [say (x1,y1)] and finding their centroids,but i cudn't go further... ... what's the next step?........Please help me out.

That irregular polygon is a triangle, and the centroid of a triangle is the point where the medians intersect.

what i meant was how to find the centroid of an irregular polygon with n sides..........i shud have mentioned the vertices as (x1,y1),(x2,y2),(x3,y3),.................(xn.yn). sorry for that.............

Originally Posted by ragsk

what i meant was how to find the centroid of an irregular polygon with n sides..........i shud have mentioned the vertices as (x1,y1),(x2,y2),(x3,y3),.................(xn.yn). sorry for that.............

I do not know the theorem from geometry which tells how to find centroid of a polygon with a compass and straightedge, if you can tell me I might be able to solve this problem.

One thing I know that this gets extremely messy, I one did it for a triangle because I was proving a theorem and the algebraic mess was collasal. But that is only for a triangle I do not know if it will get even more extreme over here I hope not.