drawing the polygon

Question

I want to draw the polygon, its sides and area is provided.
e.g.
number of sides : 4
length of 1st side : 1
length of 2nd side : 2
length of 3rd side : 3
length of 4th side : 4
area of polygon : 4.898979
please guide me how to draw the shape of the polygon.

Answer 1

Here's one option:

Label the vertices in the following way: the first vertex is the intersection of edges 1 and 4, the second vertex is the intersection of edges 1 and 2, and so on. Consider a diagonal of the quadrilateral, i.e., an edge between the first and third vertices. This makes two triangles (provided the quadrilateral is convex). Now, call $t$ the length of this diagonal, you can use Heron's formula to compute the area of the triangles and solve for $t$.

If you assume that $4.898979$ represents $\sqrt{24}$, then I plugged this into Maple and found that the diagonal described above is $\sqrt{385}/7$ (which is not a particularly useful answer, but it can be used to draw the quadrilateral.