Need a way to represent area with information about it's shape.

I am working on a version of bin packing for shapes and area. Consider a rolled out cookie dough sheet (Rectangle) and you have different sizes and shapes of cookie cutters and suppose I used say a Circle and a triangle. I have a Square cookie cutter left I need a method to find whether I have enough area left to accommodate a square, bear in mind that just a scalar value of remaining area won't do. (eg. thin and long strip has large area but won't fit a med-sized square). I need a method to represent that remaining area through which I can get information about it's structure and whether it can contain some other structure(cookie cutter). I need to calculate fitness of a particular arrangement