Construction problem

[ins-]

Construct a quadrilateral by given lengths of the 4 sides and its area.

[waxtep]

ugly analytical way: introduce two opposite angles of the quadrilateral as unknowns, write down expressions for quadrilateral area and diagonal not belonging to these angles. But there should be something nice and geometric, right?

[ins-]

In the past I found a solution to this problem in a book, but is very long:
https://www.math10.com/f/viewtopic.php?p=57918#p57918
Another approach I thought about is:
https://en.wikipedia.org/wiki/Quadrilateral
On the last page there is a formula for the area expressing it in terms of the four sides and one of the angles. In this way it is possible to calculate the angles and the construction is easier.
It seems that there is not a nice and short geometric solution to this problem.