How to pack polygons inside another polygon?
This belongs to an optimization class of problems called Packing problems. In your case, instead of a regular polygon as container, you've got an irregular one, but the idea remains the same.
These optimization problems are usually NP-hard, so I don't think there is an easy way to get the exact solution and trying all the combinations would be too too expensive.
There are some people interested in this kind of problems; I've found this link of some solved specific packing problems: https://erich-friedman.github.io/packing/
The easiest way I see, is to define an approximate center of the leather sheet, to move the set of polygons to there and, by scaling up and down and checking if the set of polygons is or not inside the target polygon, to get a closer and closer scale factor 'f' for your desired set of polygons.
But, unless you are going to use this factor for a large scale juggling balls production, probably doing it by hand would be fairly enough.