For a class project, students were asked to design a pillowcase that would fit a frilly border of 24 inches around the edge. When the project was finished, two friends were comparing their results and found that they had different pillows. The first student made a rectangular pillow, while her friend made one that was perfectly square. She was convinced that her pillow was correct and her friend had made a mistake. The second student, however, knew his was correct and wondered if it wasn't possible to have 2 different pillows with the same distance around the outside. Which student do you agree with? Why?

The second student is correct. It is possible for a polygon to have 2 different areas, but have the same perimeter. With these requirements, there are many options!

The only specification was that the pillow had to have a perimeter of 24 inches. So, there are several options:

	6 in.
		6 in.
			10 in.
		2 in.