Suppose We are given the length of all six sides of a Convex Hexagon. How can we tell whether it's valid or Not ? that means can we tell whether it's area is positive or not ? 



Determining A valid Convex Hexagon given The length of Six sides
A chain of edges can close iff the longest edge is not longer than the sum of the lengths of all the other edges. This is Theorem 8.6.3 (p.326) in [*Computational Geometry in C*](http://cs.smith.edu/~jorourke/books/compgeom.html) and Theorem 5.1.2 (p.61) in [*Geometric Folding Algorithms*](http://gfalop.org/). You can easily see the necessity of this condition: If one edge $e$ is too long, the others all together cannot reach from end-to-end of $e$.


This result has nothing to do with $6$; it holds for $n \ge 3$ edges.


