Second moment area of symmetrical shape

[fosternn]

Homework Statement

-a beam with square cross section, side lengths bXb is rotated 45 degree.
-can we assume the second moment area (I) is the same if this is done?

Homework Equations

I=b^4/12 (cube)
I=integral(r^2dr)

The Attempt at a Solution

 

[pongo38]

If you know how the formula I=b^4/12 (cube) has been derived from an integral, then you should be able to do the same for the diamond shape. Or, if you accept the formula for a triangle and apply the parallel axis theorem, you can answer the question yourself. I don't see the relevance of I=integral(r^2dr).