List of centroids

The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object $$X$$ in $$n$$-dimensional space is the intersection of all hyperplanes that divide $$X$$ into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of $$X$$. For an object of uniform composition, or in other words, has the same density at all points, the centroid of a body is also its center of mass. In the case of two-dimensional objects shown below, the hyperplanes are simply lines.

2-D Centroids
For each two-dimensional shape below, the area and the centroid coordinates $$(\bar{x},\bar{y})$$ are given:


 * Where the centroid coordinates are marked as zero, the coordinates are at the origin, and the equations to get those points are the lengths of the included axes divided by two, in order to reach the center which in these cases are the origin and thus zero.

3-D Centroids
For each three-dimensional body below, the volume and the centroid coordinates $$(\bar{x},\bar{y},\bar{z})$$ are given: