Today we will see here the method to determine the moment of inertia for the triangular section about a line passing through the base of the triangular section with the help of this post.

Let us consider one triangular section ABC as displayed in following figure. Let us assume that one line is passing through the base of the triangular section and let us consider this line as line BC and we will determine the moment of inertia for the triangular section about this line BC.
b = Width of the triangular section ABC
h = Depth or height of the triangular section ABC
IBC = Moment of inertia of the triangular section about the BC line

### Now we will determine the value or expression for the moment of inertia of the triangular section about the line BC

Let us consider one small elementary strip with thickness dy and at a distance y from the vertex of triangular section ABC as displayed in above figure.

Let us determine first the area and moment of inertia of the small elementary strip of triangular section about the line BC

Area of triangular elementary strip, dA = Width of strip (DE) x Thickness of strip (dy)
Area of the triangular elementary strip, dA = DE x dy

Let us find the value of DE by considering the two triangular sections i.e. ABC and ADE and we can easily conclude that

DE/BC = y/h
DE/b = y/h
DE = b.y/h

Therefore we can write here area of triangular elementary strip, dA = (b.y/h) dy
Moment of inertia of the triangular elementary strip about the line BC = dA. (h - y) 2
Moment of inertia of the triangular elementary strip about the line BC = (b.y/h) (h - y) 2dy

Now in order to secure the moment of inertia of the triangular section ABC about the line BC, we will have to integrate the above equation from 0 to h and therefore we can write here the moment of inertia of triangular section about the base line and we will have as mentioned here.
Moment of inertia of the triangular section about the BC line.
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### Reference:

Strength of material, By R. K. Bansal

We will see another important topic i.e.Moment of inertia for the triangular section about a line passing through the center of gravity and parallel to the base line of the triangular section in the category of strength of material.