Find the second moment, about the specified line, of each of the following areas:
A triangle ABC in which \angle ABC = 90^{o} and AB=BC=l, about AB.

I used M=x^2\delta A for this.
The triangle is represented by the axes and the line y=l-x.
With AB vertical.
\delta A=x\delta y
M=x^3\delta y
So the second moment of area about the line AB
\displaystyle =\int^l_0 (l-y)^3dy
\displaystyle =\int^l_0 (l^3-3l^2y+3ly^2-y^3)dy
\displaystyle = \left[l^3y-\frac{3}{2}l^2y^2+ly^3-\frac{y^4}{4}\right]^l_0


Answer is \frac{1}{12}l^4