Consider the following diagram of your prized 9' x 12' Persian rug:
During some recent festivities a guest spilled wine on the rug, ruining the 8 square feet depicted in red.
To remedy the problem, you intend on cutting the rug into multiple pieces, moving and possibly rotating the pieces (2D rotations only; no turning pieces over), and gluing them back together again. You can cut any way you please—vertically, horizontally, diagonally, or along any 2D curve—but you must respect three rules:
- the reassembled rug may not comprise more than two pieces
- none of the red area may appear on the reassembled rug
- the reassembled rug must be square or rectangular in shape and be a simple polygon (i.e. no holes).
Since this is indeed a very expensive Persian rug, your objective is to leave as much area as possible in the reassembled rug.
What square footage can you save, and how do you accomplish it?
Puzzlers are politely encouraged to place answers in spoiler blocks to avoid spoiling the fun for other readers. :)