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


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.

  • $\begingroup$ You mean octagon? $\endgroup$ – Mario Carneiro Feb 27 '15 at 17:18
  • $\begingroup$ yes, corrected. $\endgroup$ – Maurizio De Leo Feb 27 '15 at 17:20

Perhaps you could make some argument by inscribing a (possibly irregular) polygon with fewer than 8 sides, then use user207376's system of equations approach to separate the polygon into parts with fewer (or exactly) 5 sides. The dissection of your problem into cardinal directions would suggest such a division inscribes (or circumscribes) a square or rectangle


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