Derive the expression for the centroid of right angled triangle.

Consider the right triangle shown in Figure 1. Along the hypotenuse, y = a x.

The area of the triangle is

The x coordinate of the centroid, X, multiplied by the area is equal to the integral of x multiplied by the area da. That is, it is the sum of the small areas da multiplied by their x coordinate.

where,

Therefore,

Solving for the x coordinate of the centroid,