Centroid: It is the geometrical center of any object of figure. It is the weighted average of area of any figure. Actually it referring to a central point that represents the “average” or “balance point” of a shape, object.
For regular bodies like circle, triangle, rectangle we can easily find its geometrical center.
- For Rectangle centroid is the point located at the intersection of its diagonals, which is the midpoint of both the length and width of the rectangle.
- For circle it is the center point of the circle.
- For triangle it is the point of intersection of its three medians (lines connecting a vertex to the midpoint of the opposite side).
For irregular shaped objects it is the weighted average of its area.
Let’s assume an irregular shaped figure or object having an area A . The body can be considered as a summation of n numbers of small areas a1,a2,a3,a4……an represented by the points C,D,E,F,H,I,J …….
Now assume the geometrical mean or geometrical centre of the figure is point G is at a distance \(\overline{X}\) from the reference plane or axis.
\(\overline{X}\)= \(\frac{a_{1} x_{1}+a_{2} x_{2}+a_{3} x_{3}+ . . . . a_{n} x_{n} }{ a_{1}+a_{2}+a_{3}+. . . a_{n} }\)
where \(\overline{X}\) is the distance of centroid from the reference axis.