In order to cut your shapes in halves or quarters, you need to use the Cutter.

To cut a shape in half, place the cutter on your belt and make sure that you have two exiting belts for the resulting halves. Please note that the cutter only cuts vertically, in order to obtain a rotated half, you need to rotate your shapes.

In order to cut quarters, you'll need to position another cutter a bit further down your belt. 

For more information regarding buildings and how to use them, please check this article: 

https://shapezio.fandom.com/wiki/Buildings