Triangle - Keeping Area or Perimeter Constant
- Walter M. Stroup
Keeping area constant
Move any of the vertices and notice what happens to Area and P(erimeter). Return to a triangle about the same size (or press the undo button or refresh this page) with an Area of 2. Move a purple point to one of the vertices. Now click on middle of the triangle (to select it) and move the same vertex to a point where the triangle's Area is 2. Drag a point to this new location. Repeat for at least 8 purple points: Click the triangle again and move the same vertex to another location where the area is 2. Drag another purple point to this location. What do you notice? How could you use the tools to confirm any patterns you might see? How might this relate to the formula for the area of a triangle?
Keeping perimeter constant
Refresh this screen to reset the figure. If you want, you can move or change the triangle. The triangle you end up with should have a P(erimeter) of 6.5. As with the area earlier, move a purple point to one of the vertices of your triangle. Click the triangle and move this same vertex to a point where the P(erimeter) is 6.5. Drag another purple point to the new location of the vertex. Repeat clicking the vertex, moving it to a new location (P=6.5) and moving a purple point to this location. What pattern seems to be emerging from the collection of points? For which of the points was the Area near, or at, a maximum value? How might your results be related to the orbit of Halley's comet? https://en.wikipedia.org/wiki/Halley%27s_Comet#/media/File:Halley's_Comet_animation.gif