A=\frac{1}{2}bhVariables
- A: area
- b: chosen base length
- h: perpendicular height to that base
How to use this formula
Calculates triangle area from a base and its perpendicular height.
Important notes
- The height must be perpendicular to the base.
- Any side can serve as the base if the matching height is used.
Quick example
A triangle with base 8 and height 5 has area 20 square units.
Applicability, worked calculation, and verification
Domain and applicability
Applies to any Euclidean triangle when h is measured perpendicular to the selected base, including when the altitude falls outside an obtuse triangle.
Units
- b and h use compatible length units
- A uses squared length units
Assumptions and domain checks
- The height must be perpendicular to the base.
- For the Area of a Triangle, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- Use one consistent unit system and confirm whether lengths, areas, volumes, and angles use the dimensions implied by the formula.
Do not use this formula when
- Do not use Area of a Triangle when the stated lengths, angles, or geometric conditions do not match the figure or use inconsistent units.
Boundary and special cases
- For Area of a Triangle, check zero, negative, and extreme input values before relying on the result.
- When using Area of a Triangle, confirm that denominators, radicals, logarithms, and domain restrictions remain valid for the chosen values.
Equivalent and alternative forms
- Keep the canonical LaTeX form A=\frac{1}{2}bh for copying; rearrange only after preserving equivalence and domain restrictions.
Worked example
For a triangle with base 10 cm and perpendicular height 6 cm, A = ½(10)(6) = 30 cm².
- Choose a side as the base, b = 10 cm.
- Use the perpendicular distance to that base as h = 6 cm.
- Multiply the base and height: 10 × 6 = 60 cm².
- Divide by two to obtain A = 30 cm².
Independent verification
A rectangle with the same base and height has area 60 cm², so the triangle occupies exactly half that area.
Common mistakes
- When copying Area of a Triangle, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Area of a Triangle, 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 Area of a Triangle 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=\frac{1}{2}bh. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-26
Review method: Reviewed the notation, variable definitions, applicability conditions, worked workflow, and verification method for Area of a Triangle.
Verified against: OpenStax Algebra and Trigonometry
Automated quality check: Passed the core formula indexing gate.
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 Area of a Triangle used for?
Calculates triangle area from a base and its perpendicular height.
Can I copy this formula as LaTeX?
Yes. Copy A=\frac{1}{2}bh 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.