Triangle: properties & formulas
Three straight sides enclose the simplest polygon. A triangle’s angles total 180°, and its area depends on a base and its perpendicular height.
- 3 sides
- 3 vertices
- 180° angle sum
- 0 diagonals
Properties of a triangle
| Sides / vertices | 3 / 3 |
|---|---|
| Interior-angle sum | 180° |
| Exterior angle | Equals the sum of the two opposite interior angles |
| Triangle inequality | Any two sides add up to more than the third |
| Angle types | Acute, right, or obtuse |
| Side types | Equilateral, isosceles, or scalene |
Triangle formulas
| Area | A = bh / 2 |
|---|---|
| Area from three sides | A = √[s(s − a)(s − b)(s − c)] |
| Perimeter | P = a + b + c |
| Angle sum | A + B + C = 180° |
| Right triangle | a² + b² = c² |
Triangle area calculator
Give your shape a size.
Use the same unit for every dimension. Changing the unit relabels the measurements; it does not convert them.
From dimensions to an answer
A worked example
A triangle with base 8 and perpendicular height 5 has area 20 square units. Its other sides cannot be determined from these two measurements alone.
Triangle: common questions
Wondering about the why? Start here.
What are the types of triangles?
By sides: equilateral (three equal sides), isosceles (at least two equal sides), and scalene (no equal sides). By angles: acute (all angles under 90°), right (one 90° angle), and obtuse (one angle over 90°). Every triangle has one label from each list.
Discover triangle typesCan I use a sloping side as the height of a triangle?
Only if that side is perpendicular to your chosen base. In A = bh/2, height means the perpendicular distance from the opposite vertex to the line containing the base. In an obtuse triangle, that height may lie outside the triangle.
Understand the area formulaHow can I find area if I only know the three side lengths?
Use Heron’s formula: A = √[s(s − a)(s − b)(s − c)], where s = (a + b + c)/2. The side lengths must form a valid triangle. Choose SSS in the triangle solver to calculate it with worked steps.
Calculate from three sides