Geraldine and Suzanne sent in their
solutions to this problem. They said:
We think there are five
different squares which you can make on a 4 by 4 geoboard. Here
is a picture of three of them:
Here is a picture of the other two which only have pegs at their
corners, not along their sides:
The pink square in the second picture has an area of two square
units. We don't think you can make a square with an area of three
square units as the next size up square we have has sides of 2
which means its area is 4 square units (too big).