How to divide a shape into more than two parts at once in Inkscape?

Question

inkscape

The essence of the problem is the following, I create a rect after which I need to divide it into several polygons, for example into four parts, I draw a line above it and cut it along the line, first into two parts, and then I have to work with each part separately. If you draw several lines at once above the figure, then you will not be able to divide by them.
So I would like to know how to do it right, if possible, so that it would be easier to divide the figures into parts at once.
Thank you!

Answer 1

If you draw a bunch of intersections with one line, then it works quite well.
I've broken the pieces down a bit to make it clearer.