Heron's formula: triangle area from three sides
Heron's formula gives the area from the three sides alone: √(s(s−a)(s−b)(s−c)), where s = (a + b + c)/2 is the semiperimeter. No angle is needed, which makes it the one to use for SSS. If any factor comes out negative, the three lengths cannot form a triangle.
Related Area identities
Common questions
What is the Heron's formula identity?
Heron's formula gives the area from the three sides alone: √(s(s−a)(s−b)(s−c)), where s = (a + b + c)/2 is the semiperimeter. No angle is needed, which makes it the one to use for SSS.
When do you use the Heron's formula identity?
If any factor comes out negative, the three lengths cannot form a triangle.
Which identities are related to Heron's formula?
Heron's formula belongs to the Area group. The identities used alongside it most often are SAS area.
Practise it
Reading a formula is not the same as recalling it under time pressure. The workspace drills Area questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.
Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.