Triangle Calculator
Calculate area and perimeter of triangles. Enter values for instant results with step-by-step formulas.
Worked Examples
Example 1: Simple Area
Problem:Base=10, Height=5
Solution:0.5 × 10 × 5
Result:25
Example 2: Perimeter
Problem:Sides 3, 4, 5
Solution:3 + 4 + 5
Result:12
Frequently Asked Questions
What is the sum of angles in a triangle?
The sum of the interior angles of any triangle in a flat plane is always 180 degrees (or π radians).
What is a Right Triangle?
A triangle containing one 90-degree angle. The side opposite the right angle is called the hypotenuse, and the Pythagorean theorem (a² + b² = c²) applies.
What is an Isosceles Triangle?
A triangle with at least two sides of equal length. The angles opposite the equal sides are also equal.
What is a Scalene Triangle?
A triangle where all three sides have different lengths, and all three angles are different.
What is an Equilateral Triangle?
A triangle where all three sides are equal. All angles are also equal (60 degrees each).
Can a triangle have two right angles?
No. Since the sum of angles must be 180°, two 90° angles would leave 0° for the third angle, which is impossible in Euclidean geometry.
What is the Triangle Inequality Theorem?
It states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Otherwise, the sides won't connect.
How are triangles used in construction?
Triangles are the strongest shape because they cannot be deformed without changing the length of a side. This is why trusses and bridges are built using triangular patterns.
What are special right triangles?
Special right triangles have fixed side ratios that make calculations exact without a calculator. In a 45-45-90 triangle (an isosceles right triangle), the two legs are equal and the hypotenuse is leg × √2. If each leg is 1, the hypotenuse is √2 ≈ 1.414. In a 30-60-90 triangle, the sides are in ratio 1 : √3 : 2, where the shortest side is opposite the 30° angle and the hypotenuse is twice the shortest side. These triangles appear constantly in engineering, architecture, and physics — for instance, a roof pitch of 45° forms a 45-45-90 triangle, and an equilateral triangle bisected diagonally creates two 30-60-90 triangles. Knowing these ratios eliminates the need for trigonometric tables in common scenarios.