Sketch all of the arrangements that Jack could make with his tiles so that all of the tiles touch at least one other tile completely along a side. Assume that no tiles can overlap. How many arrangements are there?
Can you find at least
different arrangements without counting those that are simply rotations or reflections of each other?
For each diagram that you drew in part (a), find the area (the “tiles”) and the perimeter (the “toothpicks”). What do you notice?
The area is the number of tiles while the perimeter is the number of toothpicks surrounding the tiles.