[Math] How to draw an irregular polygon given all the side lengths and total area, but no angles

areapolygons

I need to draw a sketch of an irregular piece of land where I know the 8 side-lengths and the total area, but I have no information on the interior angles. The description of the terrain is as follows:

  • NORTH DIMENSIONS (3 sides):
    Side 1 – 258.40 Mts;
    Side 2 – 69.15 Mts;
    Side 3 – 136.00 Mts.

  • SOUTH DIMENSIONS (4 sides):
    Side 4 – 173.21 Mts;
    Side 5 – 84.00 Mts;
    Side 6 – 40.00 Mts;
    Side 7 – 271.76 Mts.

  • WEST DIMENSIONS (1 side):
    Side 8 – 79.57 Mts.

  • TOTAL AREA: 31,093.8598 Mts2.

I guess it's safe to assume that the polygon is convex.

Thank you

Best Answer

You have too many degrees of freedom. The length of the sides and the area are enough to determine the configuration for a pentagon but not for an octagon.

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