LaTeX
A=\sqrt{s(s-a)(s-b)(s-c)},\quad s=\frac{a+b+c}{2}Variables
- a,b,c: side lengths
- s: semiperimeter
How to use this formula
Calculates triangle area from its three side lengths.
Important notes
- The side lengths must satisfy the triangle inequality.
Quick example
Sides 3,4,5 give area 6.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The side lengths must satisfy the triangle inequality.
- For the Heron Formula, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For a real-valued result, each even-root radicand must be nonnegative unless complex values are intended.
- Use one consistent unit system and confirm whether lengths, areas, volumes, and angles use the dimensions implied by the formula.
Worked example
Sides 3,4,5 give area 6.
Common mistakes
- When copying Heron Formula, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Heron Formula, do not report a length, area, or volume with the wrong unit dimension, and keep intermediate precision until the final rounding step.
Continue the workflow
Use Heron Formula in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
A=\sqrt{s(s-a)(s-b)(s-c)},\quad s=\frac{a+b+c}{2}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Heron Formula used for?
Calculates triangle area from its three side lengths.
Can I copy this formula as LaTeX?
Yes. Copy A=\sqrt{s(s-a)(s-b)(s-c)},\quad s=\frac{a+b+c}{2} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.