Calculate the area of a triangle from its three side lengths alone — no angle or height needed.
Heron's formula gives the area of any triangle directly from its three side lengths a, b and c. First the semi-perimeter (s) is calculated, then the area itself:
The formula is named after Heron of Alexandria, who described it around 60 AD — though there are indications it was known earlier. It's especially useful when you know all three sides but not any angle or height, since the alternative (½ × base × height) isn't directly applicable then.
Use Heron's formula when you know all three side lengths but not the height. If you know the base and height directly instead, ½ × base × height is both simpler and faster.
Because the three sides can't form a valid triangle — the sum of the two shortest sides must always be greater than the longest side (the triangle inequality). If it's equal to or less, the triangle "flattens" into a straight line or can't close at all.
Yes, Heron's formula works for any triangle — right, isosceles, equilateral, or scalene — as long as the three side lengths are valid.