Undergrad Resolve moment of inertia at an angle

[curiousPep]

Initially, I calculate the moment of inertia of of a square lamina (x-z plane). Thr this square is rotated an angle $\theta$ about a vertex and I need to calculate the new moment of inertia about that vertex.

Can I split the rotated square to two squares in the x-z plane and y-z plane to find the matrix of moment of inertia about x,y,z axis and then use the rotated shape and the parallel axes theorem to find the moment of inertia abou the vertex?
What I mean is resolving the the dark shape to two shapes (red and orange outline) and find the individual moment of inertia to find the moment of inertia of the dark shape

 

[osilmag]

You might be a little off if you split it into two planes. You will have to use a triple integral.
You can find that here: https://www.physicsforums.com/threads/moment-of-inertia-about-tangent-of-a-hoop.828760/

 

[curiousPep]

You might be a little off if you split it into two planes. You will have to use a triple integral.
You can find that here: https://www.physicsforums.com/threads/moment-of-inertia-about-tangent-of-a-hoop.828760/

I see, but when can I use the two planes method?