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Geometry & Practical Projects

Triangle Area Calculator

Calculate a triangle’s area from base and height, three sides (Heron’s formula) or two sides and the included angle.

Your inputs

Results

Area

30 m²

✓Exact calculation — rounded only for display

What this calculator does

Choose whichever measurements you have; all three methods give the same area for the same triangle.

Formula and method

Area = ½ × base × height; Heron (stable form): ¼√((a+(b+c))(c−(a−b))(c+(a−b))(a+(b−c))) with a ≥ b ≥ c; SAS: ½ab sin C

Worked example

Calculated by this tool with its default inputs:

Inputs

  • Length unit: Metres
  • I know: Base and height
  • Side a / base: 10
  • Side b / height: 6

Results

  • Area: 30 m²

How to read the results

Three sides must satisfy the triangle inequality.

Assumptions and limitations

  • Use one length unit consistently; areas are in square units and volumes in cubic units of that length.
  • The stable form of Heron’s formula avoids precision loss for very thin triangles.

Quantities and costs are planning estimates. Add sensible allowances, and check with suppliers, carriers or professionals before buying, shipping or building.

Questions

What is the triangle inequality?

The two shorter sides must add up to more than the longest side.

Methodology and verification

Result type
Exact mathematical calculation (rounded only for display)
Formula version
1.0
Automated verification
4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
Editorial review
Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.

Privacy

Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy