Bretschneider's formula gives the area of a quadrilateral, , by the following formula:
Notation: Let represent the area of a polygon (here, a triangle or a quadrilateral). Also let , and let , , , . Let be the semiperimeter of the quadrilateral , given by .
Construction: Join .
Now we will use cosine rule to find in two ways, once using and once using .
Squaring and adding equations and , we have
which is the Bretschneider's formula.