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You could do it a few different ways, but I would cut the rectangles, switch to Draw Inside mode, and paste in place.
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That would be whatever shape you pasted the rectangles into. It doesn't have to be one of your visible shapes--it could be a shape with a fill/stroke of None.
Let me know if this makes any sense--it IS Friday...
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There are so many ways to do this. I suggest you learn all of these, in this order.
Pathfinder - https://design.tutsplus.com/tutorials/illustrator-in-60-seconds-how-to-use-the-pathfinder-tool--cms-...
Clipping Masks - https://helpx.adobe.com/illustrator/using/clipping-masks.html
Opacity masks - https://helpx.adobe.com/ie/illustrator/how-to/illustrator-opacity-masks-transparency.html