While contemplating ways to extend the author's ninth-grade honors geometry students' thinking and knowledge about area and perimeter, he discovered an interesting type of problem based on Erickson's (2001) rectangle problem, which he had been using for ten years. Erickson's original problem involves creating random rectangles with lengths and widths between 0 and 10 and investigating the scatter plot of area versus perimeter. In this article, the author discusses how to investigate the problem and how students can explore interesting area and perimeter problems using a 6-inch-square sheet of paper and a simple rule for creating a polygon. (Contains 11 figures.)