This is probably a stupid question but if I have the number of sides of an irregular shape and the length of each side is there a way to find out the area the shape without knowing what the shape is? i.e. I cannot use the method of breaking the shape into small regular shapes such as rectangles, triangles, etc. to calculate the total area.

The only information I have is the number of sides and the length of each side. Many thanks for any help!

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    $\begingroup$ Unfortunately, it's not enough information at all. To see why, consider a regular hexagon with all lengths the same, and then 'pull' two of its opposite vertices outward. The number and length of the sides doesn't change, but the hexagon flattens and therefore loses area. $\endgroup$ – Semiclassical Jul 30 '14 at 4:08
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    $\begingroup$ Put "hinges" at the corners of a square. You can turn the square into a rhombus with unchanged side lengths, but arbitrarily small area. $\endgroup$ – André Nicolas Jul 30 '14 at 4:27
  • $\begingroup$ Ah ok, I was thinking it could not be done but was unsure why. Your explanations have helped. Many thanks to all! $\endgroup$ – bennythemink Jul 30 '14 at 5:36

Draw a picture and you will be convinced.

enter image description here

  • $\begingroup$ Many thanks iHubble! It makes perfect sense. $\endgroup$ – bennythemink Jul 30 '14 at 5:36

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