Triangle Area Calculator
The formula
Area = base × height ÷ 2
The height must be perpendicular to the base: it is the distance from the base to the opposite corner, measured at a right angle — not the length of a sloping side.
Worked examples
- Base 8 m, height 5 m: 8 × 5 ÷ 2 = 20 m² — for example the gable end of a house, to work out how much cladding or paint it needs.
- A right triangle with sides 3 cm and 4 cm around the right angle: the two short sides are base and height, so the area is 3 × 4 ÷ 2 = 6 cm².
A triangle is exactly half of a rectangle (or parallelogram) with the same base and height, which explains the division by 2.
When you know the three sides: Heron's formula
If you don't know the height, use the three side lengths a, b and c:
- Semi-perimeter: s = (a + b + c) ÷ 2
- Area = √(s × (s − a) × (s − b) × (s − c))
For sides 5, 6 and 7 m: s = 9, area = √(9 × 4 × 3 × 2) = √216 ≈ 14.7 m². This is handy for an irregular plot of land measured with a tape.
Other cases
| What you know | Formula |
|---|---|
| Base and height | b × h ÷ 2 |
| Three sides | Heron's formula |
| Two sides and the angle between them | ½ × a × b × sin(angle) |
| Equilateral triangle of side a | a² × √3 ÷ 4 |
An equilateral triangle with 10 cm sides has an area of 100 × 1.732 ÷ 4 = 43.3 cm².
Splitting complex shapes
Any polygon can be divided into triangles. To measure an irregular room or field, split it into triangles from one corner, calculate each area and add them up. Use the rectangle and trapezoid calculators for the parts that have those shapes.
Frequently Asked Questions
Which side is the base?
Any side can be the base, as long as the height is measured perpendicular to that side from the opposite corner.
How do I find the area with only the three sides?
Use Heron's formula: s = (a + b + c) ÷ 2, then area = √(s(s − a)(s − b)(s − c)).
What is the area of a right triangle?
Half the product of the two sides that form the right angle. With legs of 6 and 8, the area is 24.