¥ The
task began with a homework problem. It is taken from Reconceptualizing Mathematics: Courseware for Elementary and Middle School Teachers, *Center for **Research
in Mathematics and Science Education*,
1998.

¥* *

¥* **Is there a relationship between the area and the **perimeter of a polygonal shape made with congruent **square regions?** *(For fixed area, find the minimum and maximum perimeter. For fixed perimeter, find the minimum and maximum area.)* Squares must be joined **complete-side
to complete-side. The outside ÒboundaryÓ **should be a polygon. In particular, this would not
permit **a shape with a ÒholeÓ in the
middle.*