List of centroids

The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object formula_1 in formula_2-dimensional space is the intersection of all hyperplanes that divide formula_1 into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of formula_1. For an object of uniform composition, 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 formula_5 are given:
3-D Centroids.
For each three-dimensional body below, the volume and the centroid coordinates formula_6 are given: