Free · Triangle calculators 🔺

Triangle Area from Three Sides and Obtuse Inverse Branch

Calculate triangle area from three sides and obtuse inverse branch with converted units, positive geometric inverses and explicit model limits.

  • Formula & worked example
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Calculator inputs

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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

Sides 3, 4 and 5 cm form a right triangle with area 6 cm².

s = (a+b+c)/2; A = √[s(s−a)(s−b)(s−c)]

Worked example

Enter these known values and leave the other values blank.

a
3 cm
b
4 cm
c
5 cm
Area
6 cm²

Assumptions and limitations

  • Each side is positive and any two sides sum to more than the third. Recovering a third side from area and two sides can have two answers; the retained inverse selects the larger third side (the obtuse included-angle branch), with the right-angle boundary shared.
  • Measurements must describe the same shape. Clear a quantity you want to infer instead of supplying conflicting measurements. Unit selectors are converted before the geometric relationships are applied.
  • Calculations use 64 significant digits with full-precision π; result formatting rounds the displayed value separately. These are ideal geometric models, without material allowances or measurement uncertainty.
  • Very flat triangles amplify measurement rounding. The result uses the supplied side lengths and cannot recover precision absent from the measurements.

Common questions

Why might an inverse side result differ from my original triangle?

An area and two sides determine the sine of the included angle. Acute and obtuse angles can share that sine. This captured inverse chooses the obtuse branch and hence the larger third side; it does not recover both possibilities.

References

Require real, positive geometric inverses and the stated shape domain before displaying derived results. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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