How this calculation works
Apply Bretschneider’s formula when the quadrilateral is not assumed cyclic.
THE FORMULA
A²=(s−a)(s−b)(s−c)(s−d)−abcd cos²[(A+C)/2]A worked example
Four equal sides of 4 and opposite angles summing to 120° give area 8√3.
Good to know
Use a convex quadrilateral with compatible measurements.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Apply Bretschneider’s formula when the quadrilateral is not assumed cyclic.
The primary result is labeled “Area”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Use a convex quadrilateral with compatible measurements.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Four equal sides of 4 and opposite angles summing to 120° give area 8√3.
Which rule does this calculator apply?
A²=(s−a)(s−b)(s−c)(s−d)−abcd cos²[(A+C)/2]