Triangle Area from Three Sides
Area, perimeter and height of a triangle when you only know the three side lengths.
Results
Area
26.8328
m²
Perimeter
24.000
m
Semi-perimeter
12.000
m
Height
7.6665
m
What this tool does
Heron's formula is what surveyors use, because measuring three sides with a tape is far easier than measuring a perpendicular height. Any irregular plot of land can be split into triangles, measured side by side, and added up.
Formula
s = (a+b+c) ÷ 2 , A = √(s(s−a)(s−b)(s−c))
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a | Side a | m |
b | Side b | m |
c | Side c | m |
A | Area | m² |
P | Perimeter | m |
S | Semi-perimeter | m |
H | Height | m |
Worked example
- Side a7 m
- Side b8 m
- Side c9 m
- Area26.8328 m²
- Perimeter24.000 m
- Semi-perimeter12.000 m
- Height7.6665 m
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.