This activity invites you to compare sizes of some of your Geometiles shapes.

By **size**, we mean the areas of the pieces; more specifically, the areas of the squares and rectangle outlined in black above. Which is the largest? Which is the smallest?

The answers to some of these questions are pretty straightforward. For example, it’s pretty clear that the purple square is smaller than the orange one. You can also overlay the green rectangle and the orange square and find that the orange square is larger:

The rectangle outlined in purple is larger than the one outlined in yellow.

How do we compare the sizes of the purple square and green rectangle? Let’s just measure them with your ruler.

The green rectangle is approximately 4.9 cm wide and 8.4 cm tall. The purple square has side length 6 cm. You can guesstimate that 4.9 X 8.4 is at least 40 (think 5 X 8), but 6 X 6= 36. So the green rectangle is larger than the purple square.