The Area Of A Triangle Calculator

A triangle covers exactly half of whatever parallelogram shares its base and height. Nearly every wrong answer comes from one of two slips: a height that was never perpendicular, or a base and a height borrowed from two different sides.

BaseAny one side you choose to measure from.Height to that basePerpendicular distance from the base to the opposite corner — not the length of a slanted side.Side AUsed only when working from three sides.Side BSide CWhat you knowPick the measurements you actually have, not the ones you wish you had.

Area of the triangle

Perimeter from the three sides: 24
Semi-perimeter used by Heron's formula: 12
Area from the three sides alone: 26.8328

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

Area = 1/2 x base x height

base: Any one side of the triangle, chosen by you
height: Perpendicular distance from that base to the opposite corner
a, b, c: The three side lengths, used when no height is known
s: Semi-perimeter, equal to (a + b + c) / 2
A: Enclosed area, always in square units

How to check the result by hand

1
Choose a base and stay with it
Any of the three sides works and the area does not depend on which you pick. In a triangle with sides of 7, 8 and 9, taking 8 as the base is convenient because the height to it is 6.70820393.
2
Measure the perpendicular height to that base
Shortest distance from the base's line to the opposite corner, at a right angle. With a base of 10 and a slanted side of 7, the true height of 6 is the one to use; the slanted side would give 35 instead of 30.
3
Multiply the two lengths, then halve
10 x 6 = 60, and half of that is 30. Halving last keeps the intermediate figure comparable with the parallelogram the triangle sits inside.
4
If you only have the sides, switch to Heron's formula
Add the three sides and halve to get s, subtract each side from s, multiply the four values and take the root. For 7, 8 and 9: s = 12, the product is 720, the area is 26.83281573 and the perimeter is 24.
5
Attach square units and round once
A base and height in metres give square metres. If the inputs were measured to the nearest unit, quoting 26.83281573 overstates what was known; 26.8 or 27 is the honest figure.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Area Of A Triangle page.