How this calculation works
Find the area of a convex quadrilateral from diagonal lengths and their intersection angle.
THE FORMULA
A=d₁d₂ sin θ/2A worked example
Diagonals 10 and 8 meeting at 30° give area 20.
Good to know
The diagonals must cross inside the quadrilateral.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the area of a convex quadrilateral from diagonal lengths and their intersection angle.
The primary result is labeled “Area”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The diagonals must cross inside the quadrilateral.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Diagonals 10 and 8 meeting at 30° give area 20.
Which rule does this calculator apply?
A=d₁d₂ sin θ/2