The sidelengths are given at the beginning or by clicking New Polygon below. Drag the slider to change the area.
The construction is explained in www.pnas.org/content/108/37/15053.full
Vertices (u1,v1) and (u2,v2) are given by the intersection of the circle of radius b and centre at the origin and a line that depends on sidelengths and area.
If one specifies an area larger than the maximum area, no quadrilateral exists.
If the area specified is exactly equal to the maximum area then there is one quadrilateral.
If the area is smaller than the maximum then there are two possible configurations.
The dotted circles are circumcircles of points ABC and AB'C'.
Is there a minimum value for the area?
What happens to the circle and line when the quadrilateral is impossible (one side is larger that the sum of the others)?
Drag the slider for Area and observe what happens.
Last change July , 2023.
All graphics created with JSXgraph.