Draw a Picture #1
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!