Triangle area is one of 5 triangles formulas in the geometry section of this library, and it is used at middle school level.
Why triangle area works
A triangle is exactly half of a parallelogram. Copy the triangle, turn the copy upside down, and fit the two together along a common side: the result is a parallelogram with the same base and the same height, covering base times height, so one triangle covers half of that.
What each symbol means
$b$ is a chosen base and $h$ is its perpendicular height.
Triangle area: when it holds
$b,h\ge0$ and height must meet the base line at $90^\circ$.
When it stops applying
The height must be perpendicular to the exact base you chose. In an obtuse triangle that perpendicular lands outside the triangle, on an extension of the base line, and the formula only works if you measure to that extended line rather than stopping at the corner.
Triangle area: a worked example
With $b=12$ and $h=7$, $A=42$ square units.
The mistake to avoid
What people do: Measuring the height along one of the slanted sides.
Why it goes wrong: A slanted side is always longer than the straight-down distance to the base line, so the area comes out inflated.
Do this instead: Draw the perpendicular from the opposite corner down to the base line and measure that segment instead.
Triangle area: step by step
- Name the unknown, and the unit the answer has to come out in.
- Match the symbols to your values. $b$ is a chosen base and $h$ is its perpendicular height.
- Check the conditions before substituting. $b,h\ge0$ and height must meet the base line at $90^\circ$.
- Substitute, keep exact values to the last line, then test the sign, size, and unit against a rough estimate — the check that catches most geometry slips.
Where this formula fits
- Subject
- Geometry formulas — 30 entries in this library
- Topic
- Triangles
- Level
- Middle school
Formulas are easiest to keep when they sit inside a method rather than on a list. Use the links below to see where triangle area comes from, to check a calculation against a tool, and to practise it until you can recall it without looking.
- Area of a Triangle — the lesson behind this formula: choose a base-height, trigonometric, or side-length formula.
- Geometry Calculator — check your substitution and the value it produces.
- Study geometry — the subject guide that explains the ideas these formulas compress.
- Geometry Practice — questions that make you retrieve the formula instead of recognising it.
- All 30 geometry formulas — the full grouped reference, or the complete formula library.
Questions about triangle area
Does it matter which side I pick as the base?
No. Each of the three sides comes with its own matching perpendicular height, and all three pairings give exactly the same area.
What if I know the three sides but no height?
Use Heron's formula, which needs no height at all, or recover a height first with the Pythagorean theorem before using this rule.
Can I use two sides and the angle between them?
Yes. Half of the product of those two sides multiplied by the sine of the angle between them gives the same area.
Why is the answer measured in square units?
Base and height are both lengths, and multiplying two lengths produces an area, so centimetres times centimetres become square centimetres.