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Area

Heron's formula: triangle area from three sides

Area=s(s−a)(s−b)(s−c),  s=a+b+c2\text{Area} = \sqrt{s(s-a)(s-b)(s-c)},\ \ s = \tfrac{a+b+c}{2}

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.

areaheron

Related Area identities

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.

Practise AreaOpen the triangle solver

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.