Triangle Calculator

Inputs

Enter parameters to calculate Area, Perimeter, and missing sides/angles.

Understanding Triangles

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Identifying the properties of a triangle (sides, angles, area) is fundamental in trigonometry and construction.

Common Formulas

Area (Base & Height)

The most common formula, used when the base and vertical height are known.

Area = ½ × base × height

Area (Heron's Formula)

Used when all three side lengths (a, b, c) are known. First, calculate the semi-perimeter (s).

s = (a + b + c) / 2Area = √[s(s-a)(s-b)(s-c)]

Law of Cosines (for Side c)

Used in SAS (Side-Angle-Side) cases.

c² = a² + b² - 2ab cos(C)

Types of Triangles

  • Equilateral: All 3 sides are equal. All angles are 60°.
  • Isosceles: 2 sides are equal. The angles opposite those sides are equal.
  • Scalene: No sides are equal. No angles are equal.
  • Right Angled: Has one 90° angle. Follows a² + b² = c².

Frequently Asked Questions

What if the SSS inputs don't make a triangle?

For three sides to form a triangle, they must satisfy the Triangle Inequality Theorem: the sum of any two sides must be greater than the third side (a + b > c).

How do I find angles?

If you know all 3 sides, the calculator uses the Law of Cosines to reverse-calculate each angle.

Can I solve if I only have 3 angles?

No, you need at least one side length to determine the size of the triangle. Three angles (AAA) only proves similarity, not congruence (size).

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