Geometry
Triangle area from three sides (Heron's formula)
The semi-perimeter lets you solve for the area without knowing any angle.
The Formula
area = sqrt(s x (s - a) x (s - b) x (s - c)), with s = (a + b + c) / 2
The semi-perimeter lets you solve for the area without knowing any angle.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| A | Triangle area | square length units | The area of the cross-section. |
| s | Semi-perimeter | same length unit | Half the sum of the three sides. |
| a, b, c | Sides | same length unit | The three sides of the triangle. |
What Each Symbol Means
Asquare length units
Triangle area
The area of the cross-section.
ssame length unit
Semi-perimeter
Half the sum of the three sides.
a, b, csame length unit
Sides
The three sides of the triangle.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the volume of a triangular prism page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Volume Of A Triangular Prism, filed under Math. Every number the guide produces comes from substituting into this one line.