Thanks for the image. First of all, there is a measuring tool inside of Cinema 4D. Main Menu> Tools> Measure and Construct. One could also use the Distance node in XPresso, or just subtract one vector from another, but I digress.
The center of gravity is typically the most used technique, also called the Plumb-Line method. (Irregular Polygons are not really considered to have a center-point, hence why they are called irregular.) One has to pick up a randomly shaped cardboard and let it hang freely. From the anchor point, a straight line down is drawn. Then this procedure is repeated from another location. Where those lines meet, there is the point of gravity. This can be done in C4D, but it also seems way over the top, in terms of effort.
A more automated process
We all might remember the Cloner Object setting Mode>Object and its Polygon Center option. Yes, that would give you something, but you asked for a precise method, and this isn’t one. I have set up an example file to demonstrate this.
The Weld Points comes to mind, as there is a central function, but also here, each point has an influence on the result. Which means, that extra points that were added to a straight edge will not change the shape, but the outcome of the point welding will. Similar to that is the Axis Center, it doesn’t really care about the center of gravity.
In the Wiki page (link above) you will find some formulas, but I guess that is beyond the scope of the project. Yes, I checked as well in the “Mathematics for Computer Graphics” book, from John Vince, but he stops short with a triangle example of this problem.
As a side note: The middle point of a polygon has to be on its surface? How about a C-shape (n-gon)for that matter?
I would go with the Cloner Object and perhaps eyeball it.
The question about the dimension, as seen in the image: This is a simple question of setting up the Grid. Select the polygon you like to measure, and then Set the Work-plane to selection. The Coordinates (not the one of the object) will give you the size between points and their position. Set it to World!
All the best
Edited 01:50pm PST