Area moments of inertia for a filled triangular area with respect to an axis through the centroid

Description

The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis.
The second moment of area for a shape is easier to be calculeted with respect to a parallel axis or with respect to a perpendicular axis through the centroid of the shape.
Area moments of inertia of a filled triangle with respect to an axis through the centroid and parallel to the shape, is depended on the base width and the height of the triangle.