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I have only lengths for the sides of an irregular polygon, can anyone tell me how I can measure the area of the polygon? Remember only lengths of all the sides, no angles or coordinates.

Few forums mention about trangulation of the polygon etc. But I only have side lengths.

Does anybody have any feedback?

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    Some polygons have four sides of length 1. Such a polygon can have various shapes, from a square down to a long thin needle of length almost 2. Its area will range from 1 down to 0. This shows why the side lengths of any polygon of four or more sides usually do not determine its area. Therefore a formula or calculation of the type you seek does not exist.
    – whuber
    Mar 7, 2012 at 14:27
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    Another example: a concave figure (smaller area) vs convex figure (larger area), each with same perimeter.
    – sgillies
    Mar 7, 2012 at 16:41

4 Answers 4

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As Whuber has mentioned in his comment, a four sided polygon is -mathematically speaking- constrained by 5 properties at a minimum. So If you have just the four side lengths, you do not have one unique polygon. Hence you can't find its area.

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    My scenario is- user roughly digitizes the irregular polygon on the openlayers map and enters the exact lengths for each side of the polygon and I wanted the area to be calculated. Since everybody has mentioned that it is not possible to calculate area based on the side lengths, can the digitized polygon sides be adjusted according to the lengths entered and bring the polygon roughly to the nearest to what is supposed to be a correct polygon? Is it something possible in POSTGIS or SQL Server 2008? I think it is possible in Geomedia. Mar 8, 2012 at 11:07
  • The digitized points should have coordinates, which can then be used to calculate the area of the polygon. The problem with using just lengths is that angles are needed also. The points used to define the polygon can also be used to get the angles. There is a standard formula for calculating the area. mathworld.wolfram.com/PolygonArea.html Mar 12, 2012 at 12:42
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For practical purposes, the maximum area possible should be calculated and it is possible to find that area without knowing any inside angle.

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Area = |(x1y2-y1x2) + (x2y3 - y2x3) + (x3y4 - y3x4) + ........(x8y1 - y8x1) |/2

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With the information given, you cannot derive the exact area for any polygon with more than 3 sides. However, there is a formula that will allow you to derive a range for the area.

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    I'm not sure if this adds anything more, than provided in the first answer. If you could add the formula to derive the range then that would be helpful.
    – nmtoken
    Aug 29, 2017 at 16:24

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