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Calculate triangle properties from three sides. Find area (Heron's formula), angles (Law of Cosines), heights, inradius, circumradius, and triangle type.
A triangle is a polygon with three sides and three angles that sum to 180°. Properties include area (via Heron's formula), perimeter, heights, and the inradius/circumradius of inscribed/circumscribed circles.
Type
Right Scalene
Area
6
Perimeter
12
Angle A
36.8699°
Angle B
53.1301°
Angle C
90°
Height (a)
4
Height (b)
3
Height (c)
2.4
Inradius
1
Circumradius
2.5
| Type | Definition |
|---|---|
| Equilateral | All sides equal, all angles 60° |
| Isosceles | Two sides equal, two angles equal |
| Scalene | All sides different |
| Right | One 90° angle |
| Acute | All angles < 90° |
| Obtuse | One angle > 90° |
Formula
A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2A = Area of the triangle
s = Semi-perimeter = (a+b+c)/2
a, b, c = Lengths of the three sides
Worked Example
Triangle with sides 3, 4, 5
Did you know? Heron of Alexandria published his area formula in the 1st century AD, but it was likely known to Archimedes 200 years earlier. The formula works for any triangle given only its three side lengths (source: Wolfram MathWorld).
Sources
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