Bendy quad

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Problem



Bendy Quad printable sheet



Four rods are hinged at their ends to form a convex quadrilateral with sides of length $3$, $4$, $5$ and $6$ (in that order). Investigate the different shapes that the quadrilateral can take.

 

Image
An example of a quadrilateral with side lengths 3, 4, 5, 6.



What are all the possible values of the angles if the quadrilateral is convex?