How to make random polygons with texture?

Hello
I need to make random polygons.
Those polygons should have a texture inside them.

Image I have are all squared.
I need to crop them into random polygons.

I would like to do this without using mask.
Could you help me to do this?

I have sprites already(hexagon etagon and 10 12 16 and so on)
What I need to do is to add textures on the polygons.
I want to do this without using masks

The testfingerpolygons scene in my MakeGeo project does exactly this.

MakeGeo is presently hosted at these locations:

https://bitbucket.org/kurtdekker/makegeo

Thank you
I will look at them