# Area, Perimeter & Curling Up When We're Cold 01

- Author:
- Walter M. Stroup

One of the biggest challenges in the mathematics is to see how AREA and PERIMETER are two DIFFERENT quantities related to a geometric figure. This activity centers on keeping one quantity constant while the other is changed. Note: The results from this activity may help explain why animals (e.g., dogs) curl up when it is cold (or spread out when it is warm).

**Directions**: Click and drag one of the points. What happens to the values of the a, b … etc.? What happens to the Area? What happens to the Perimeter? Try moving a point to a location that changes the area but not the perimeter. Now try moving it to change the perimeter but not the area. Try doing the same with some other points or even with multiple points. Press Refresh in your browser to reset the image. Choose a challenge.

**CHALLENGE**: Choose one: [1] Constant Area: Move the points to locations that keep the AREA = 10.2. Try and find locations that make the PERIMETER as SMALL as possible (less than 18.4). [2] Constant Perimeter: Move the points to locations that keep the PERIMETER 18.4. Try and find locations that make the AREA as BIG as possible (more than 10.2).

*[A] How did you think about moving the points to improve your results? What sorts of ideas came up or were useful to you? [B] What challenge did you do and what was the best value you came up with? [C] If you were to compare the results from the other challenge, what might be the similarities or differences? You can copy the address into a different TAB and see what you get. [D] How might these results be related to why animals curl up when it is cold? Which challenge, [1] or [2] is more like what an animal is able to do?*Note: You can use the menu to save your geometric figures.