# Open Middle: Maximizing and Minimizing Area (1)

Creation of this resource was inspired by an Open Middle problem from Robert Kaplinsky.

## Here, there are 24 segments that are each 1 unit long. Move the LARGE POINTS around to create a polygon that ENCLOSES THE GREATEST AMOUNT OF SQUARES (has the greatest possible area). Be sure to use all 24 pieces!

What was the greatest possible area you were able to enclose in the app above? What else do you notice?

What is the perimeter of the polygon you created? Does this result surprise you? Explain why or why not.

## Here, there are 24 segments that are each 1 unit long. Move the LARGE POINTS around to create a polygon that ENCLOSES THE LEAST AMOUNT OF SQUARES (has the least possible area). Be sure to use all 24 pieces!

What was the least possible area you were able to enclose? What else do you notice?

What is the perimeter of the polygon you created? Does this result surprise you? Explain why or why not.