Free · Geometry and function relationships

Scalene Triangle Sides, Heights and Area

Heron’s formula gives area from three positive sides satisfying every strict triangle inequality. A scalene triangle has three unequal sides; the right-triangle mode uses perpendicular legs.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For type = 0, a = 4, b = 5, c = 6, area1 = 9.921567416492214714381059076147226596413471936559188176381254222, perimeter1 = 15.

A=√(s(s−a)(s−b)(s−c)); hₐ=2A/a

Worked example

Enter these known values and leave the other values blank.

Special triangle?
0
a
4 cm
b
5 cm
c
6 cm
ha
4.961 cm
hb
3.969 cm
hc
3.307 cm
α
41.41 deg
β
55.77 deg
γ
82.82 deg
Area
9.922 cm²
Perimeter
15 cm

Assumptions and limitations

  • Heron’s formula gives area from three positive sides satisfying every strict triangle inequality. A scalene triangle has three unequal sides; the right-triangle mode uses perpendicular legs.
  • Clear the unknown field before solving. Locks preserve known quantities; an inverse may have multiple solutions and this model selects its principal branch.
  • Numerical rounding does not describe measurement uncertainty. Extremely large arguments or near-singular inverses can exceed the available precision; use moderate values for interpretable finite results.

Common questions

How do I enter a consistent set of values?

Heron’s formula gives area from three positive sides satisfying every strict triangle inequality. A scalene triangle has three unequal sides; the right-triangle mode uses perpendicular legs.

Can I calculate a missing input?

Clear that field and provide enough independent known quantities. Output-only fields and nonunique inverse branches may need a different mode.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

Explore geometry and function relationships or browse all math calculators.