I am not sure this is going to help but anyway:
The centroid of a plane figure is similar to the Centre of Gravity of, say, a flat metal plate, the only thing is that you do not call it so because your figure has no mass!!!
The Center of Gravity is a point of your plate that has the property that if you suspend the plate through it the plate do not tend to rotate.
To find it you have to think that the position of the centroid inside the figure depends on the extent of the figure AND disposition of its area. You can use integrals to relate the coordinates of the centroid
For example for a triangle: