I thought of this investigation as I was walking home and happened to notice an unusually shaped parking lot. It made me wonder if the way the parking spots were arranged within the parking lots was the most efficient way to pack the cars in. Obviously the picture above is a sample, and you are free to choose whatever parking lot you would like to share with your students.

Question: What is the most efficient way of creating parking spots within a parking lot so that as many cars as possible are able to park in the parking lot, and so that each of these cars can leave whenever they want?

Here is a Geogebra applet I designed to allow students to explore different arrangements themselves.