Finding principal inertias for a painted area

[fabiancillo]

Hello I have problems with this exercise

For the painted area calculate inertias with respect to the x and y axes and the principal inertias

Hint:
$I_x = \displaystyle\frac{bh^3}{12}$
$I_{xy} = \displaystyle\frac{b^2h^2}{24}$

Thanks

 

[ergospherical]

Keeping in mind the superposition property of the moment of inertia, can you split this shape up into pieces and evaluate $I_x$ and $I_y$ for them separately?

 

[fabiancillo]

Keeping in mind the superposition property of the moment of inertia, can you split this shape up into pieces and evaluate $I_x$ and $I_y$ for them separately?

I am totally blocked

 

[PeroK]

I am totally blocked

That's also called a moment of inertia!

 

[fabiancillo]

Ok I'll try

 

[haruspex]

$$I_x = \displaystyle\frac{bh^3}{12}$$
$$I_{xy} = \displaystyle\frac{b^2h^2}{24}$$

Fixed the LaTeX by doubling the dollar signs.
I note you only quote equations for a triangle. Do you have any for the rectangles? If not, you'll need to cut those into triangles.
Do you know the parallel axis theorem?