* What do you notice about $(4,0)$ figures?
* Choose another particular value for $(p,i)$ and explore different shapes.
* Have you tried drawing shapes with the same area?
* What do you notice about those figures whose areas are the same?
* What ways are there of increasing the area by $1$ unit?
* Draw more figures; tabulate the information about their perimeter points ($p$), interior points ($i$) and their areas ($A$).