When I'm doing any fussy cutting, I make a "window" the size I need out of a file folder or any light weight cardboard.
By window I mean drawing the square on the cardboard, cutting it out and using the window or hole to lay over the part that I want. I draw around the inside of it with chalk or pen, depending on the color. Then I cut it out with a straight ruler. My fabrics always look like Swiss cheese. Works for me.