Quadrilaterals and Bretschneider's Formula

We talk about a formula deduced by Bretschneider in the mid-nineteenth century that not only allows the computation of areas of planar quadrilaterals, regular and irregular, but also provides a more thorough understanding of the geometry of such figures. We present one version of Bretschneider's formula and talk about its scope of application and what it can say about the possible shapes of quadrilaterals.