I'm trying to understand if you can find the perimeter of a shape given only the area of the shape. No length, width, or side.

Square: sqrt(area) * 4 (I think?)

Rectangle: Impossible?

Circle: Possible?

Oval: Impossible?

Equilateral Triangle: Possible?

Oblique or Acute Triangle: Impossible?

Trapezoid: ?

Hexagon: ?


  • $\begingroup$ No, since there are many shapes with limited area but infinite perimeter. $\endgroup$ – mathreadler Feb 12 '17 at 17:42
  • $\begingroup$ Can you give an example? And also, if those shapes are rare, what if we were to disregard those shapes? $\endgroup$ – Hatefiend Feb 12 '17 at 17:43
  • $\begingroup$ The Koch snowflake is famous. But almost any fractal has that property. nl.wikipedia.org/wiki/Koch-kromme $\endgroup$ – mathreadler Feb 12 '17 at 17:44
  • $\begingroup$ Look for shapes with different perimeters that have the same area. This is straight forward for rectangles. $\endgroup$ – Karl Feb 12 '17 at 17:44
  • $\begingroup$ @Karl Right right which is why I wrote impossible for Rectangle. So basically, if the shape has all sides of the same length, then it's possible to solve? $\endgroup$ – Hatefiend Feb 12 '17 at 17:45

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