Triangle Calculator
Calculate sides, angles, area, and perimeter of any triangle using Heron's formula and the Law of Cosines.
Heritage of geometry
The triangle is the most fundamental polygon and forms the basis for complex structures in architecture and design.
Geometric Discovery
Enter the side lengths to reveal area, angles, and triangle classifications.
Triangle Calculator
Calculate sides, angles, area, and perimeter of any triangle using Heron's formula and the Law of Cosines.
How Triangles are Calculated
A triangle is a polygon with three sides and three angles. To calculate its properties, you need to provide the lengths of all three sides. The calculator validates the triangle inequality (the sum of any two sides must be greater than the third) before computing the results.
Triangle Symmetry
Understanding triangle types like equilateral, isosceles, and scalene helps in solving complex geometric problems efficiently.
Geometric Formulas
Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2We use Heron's formula for the area and the Law of Cosines to calculate each individual angle based on the side lengths provided.
Practical Examples
Right Triangle (3-4-5)
A triangle with sides 3, 4, and 5 is a classic right-angled triangle with an area of 6 and a 90° angle.
Equilateral Triangle
If all sides are equal (e.g., 5, 5, 5), all angles will be exactly 60° and the triangle is perfectly symmetrical.