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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: ?

etc.

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    No, since there are many shapes with limited area but infinite perimeter. – 2017-02-12
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    Can you give an example? And also, if those shapes are rare, what if we were to disregard those shapes? – 2017-02-12
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    The Koch snowflake is famous. But almost any fractal has that property. https://nl.wikipedia.org/wiki/Koch-kromme – 2017-02-12
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    Look for shapes with different perimeters that have the same area. This is straight forward for rectangles. – 2017-02-12
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    @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? – 2017-02-12
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    I don't understand your comment. What has all the sides same length to do with circles for example? The area of a circle is proportional to the square of its radius whilst the the circumference is proportional ti the radius. – 2017-02-12
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    @Karl Okay well circles are a good example of something that doesn't follow that rule then. But something like a hexagon or octagon could be solved for perimeter based only on area IF all of the sides are the same length, correct? – 2017-02-12
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    The question should be rephrased as does the area of a regular polygon determine its perimeter. – 2017-02-12
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    @Karl no, that's not what I'm asking. I'm saying 'which of the following (if any) regular polygons can have their perimeter determined from only their area (and under what circumstances?)' – 2017-02-12
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    Do you know what an apothem is? That will help. Chop up the polygons into triangles. I'm not sure why you distinguish between polygons and believe the changes to the question apt. – 2017-02-12
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    @Karl How can I chop up a polygon into triangles without knowing the polygon's dimensions. I only know its' area. – 2017-02-12
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    You can find internal angles of the polygons. This gives you the Base angles of isosceles triangles. Chop each isosceles triangle into to right angles ones and determine apothem in terms of side length. – 2017-02-12

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