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

Question

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

Answer 1

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.

Answer 2

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