Paritian

Mathematics

Triangle Area from Three Sides

Area, perimeter and height of a triangle when you only know the three side lengths.

Results

Area 26.8328
Perimeter 24.000 m
Semi-perimeter 12.000 m
Height 7.6665 m
The shape, to scale
Triangle Area from Three SidesTriangle Area from Three Sides: a = 7.00 m, b = 8.00 m, c = 9.00 m, 48.19°, 58.41°, 73.40°c = 9.00 ma = 7.00 mb = 8.00 m48.19°58.41°73.40°

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

SymbolMeaningUnit
aSide am
bSide bm
cSide cm
AArea
PPerimeterm
SSemi-perimeterm
HHeightm

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.