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formulas used to locate the center of gravity or the centroid
simply represent a balance between the sum of moments of all the
parts of the system and the moment of the “resultant” for the system;.
in some cases the centroid is located at a point that is not on the
object, as in the case of a ring, where the centroid is at its center. Also,
this point will lie on any axis of symmetry for the body, Fig. 1-81.

Fig. 1-81.

36 Centroid of Some Simple Geometrical Figures

Determine the distance measured from the x axis to the centroid
of the area of the triangle shown in Fig. 1-82.

Fig. 1-82.

Consider a rectangular element having a thickness dy, and
located in an arbitrary position so that it intersects the boundary at (x,

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