Rolling out the Carpet

You have 24 square feet to carpet a room in your treehouse. The drywall that you are using for the walls are expensive, so you want the perimeter of the room to be as small as possible. However, you want to be unique, so you don't want a rectangular room. Use centimeter tiles to investigate. Each tile represents one square foot of carpet.

How many various arrangements of rooms could you make that are non-rectangular? Sketch the various shapes of rooms and calculate the area and perimeter.

What arrangements of non-rectangular rooms have a larger perimeter?

What arrangements of non-rectangular rooms have a smaller perimeter?

If you were calling a friend to describe the room with the smallest perimeter, write a description of what you would say.