Draw a Picture #1

DP #2

Hints and answers

Four 1-inch by 1-inch squares are arranged so that each square touches at least one other square. Any two squares touch each other according to these rules: They can touch on the corners or they can touch entirely across one side but not partially across a side. What are the possible perimeters of the resulting figure?

To get you started, here are a couple of ways to (legally) arrange the squares:


Since the squares are 1 inch on a side, the perimeters of the first of these figures is 10 inches, the second has perimeter 14 inches, and the third has perimeter 12 inches.

Notice that the problem does not ask you to find all possible arrangements of the squares, just all the different perimeters that can arise. Draw pictures, and look for patterns!

As always, be sure to explain the work you did to arrive at your answers!