Triangle Perimeter Formula

P = a + b + c, plus special cases

Reviewed by [email protected], Geometry Calculator Developer & Online Math Educator Last updated May 8, 2026

The perimeter of any triangle is simply the sum of its three sides. The formula P = a + b + c works for every triangle type — but for special triangles you can simplify using known relationships between sides.

The Formulas

Name Formula Notes
Any Triangle P = a + b + c Sum of all three sides.
Equilateral P = 3 × a All three sides equal length a.
Isosceles P = 2a + b a = the two equal legs, b = base.
Right Triangle P = a + b + √(a² + b²) a, b = legs; hypotenuse from Pythagorean.
45-45-90 P = leg × (2 + √2) Right isosceles. Hypotenuse = leg × √2.
30-60-90 P = a × (3 + √3) a = shortest side. Sides ratio 1 : √3 : 2.

Worked Examples

Example 1: Triangle with sides 5, 12, 13

  1. P = 5 + 12 + 13 = 30 units
  2. (Bonus: this is a right triangle since 5² + 12² = 25 + 144 = 169 = 13²)

Example 2: Equilateral triangle with side 7 cm

  1. P = 3 × 7 = 21 cm

Example 3: Right triangle with legs 6 and 8

  1. Hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10
  2. P = 6 + 8 + 10 = 24 units

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