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Triangle Area from Three Sides — result sheet
Use Heron's formula to calculate triangle area, perimeter, and the altitude to the first side.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: s = (a+b+c)/2; area = sqrt(s(s-a)(s-b)(s-c)); altitude to a = 2 * area / a.
Heron's formula finds area using only three side lengths, so no angle measurement is needed. The implementation uses a rearranged form that reduces cancellation in thin triangles. The altitude shown is perpendicular to the side entered as a, even if another side is longer.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Side a (altitude base) — units; minimum 1.0E-6; maximum 1000000000
- Side b — units; minimum 1.0E-6; maximum 1000000000
- Side c — units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Side a (altitude base) | 3 |
| Side b | 4 |
| Side c | 5 |
6 square units
Assumptions and limits
- All sides are positive and in the same unit.
- The sum of the two shorter sides must strictly exceed the longest side.
- Collinear or impossible side sets are rejected, rather than reported as zero-area triangles.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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