Encyclopedia>Geometry>Planar Figures>Triangles>Triangle Attributes>What Is the Formula for the Perimeter of a Triangle?

Now let’s learn to calculate the perimeter of a triangle. The perimeter is found by adding the lengths of all the sides of the triangle.

Formula

$$P={\text{side}}_{1}+{\text{side}}_{2}+{\text{side}}_{3}$$ |

You can calculate the perimeter of different types of triangles.

Now we’ll take a look at equilateral triangles and their perimeters. An equilateral triangle is a triangle where all sides are equal in length and all angles are equal. Since the sum of the angles in a triangle is always $180$°, each angle is equal to $180\text{\xb0}\xf73$, or $60\text{\xb0}$.

To calculate the perimeter of an equilateral triangle, you just need to know the length of one side. Since all sides are the same length, you then multiply the length of any side by 3.

Rule

All sides are of equal length in an equilateral triangle.

All angles are $60$°.

$$\text{Perimeter}=3\cdot \text{lengthofside}$$ |

Example 1

The perimeter of this equilateral triangle is

$$P=3\cdot 4\phantom{\rule{0.17em}{0ex}}\text{cm}=12\phantom{\rule{0.17em}{0ex}}\text{cm}$$ |

Now we’ll go over isosceles triangles. An isosceles triangle is a triangle with two sides of equal length. It then follows that two of the angles are equal as well. We often call the equal sides the legs, and the third side is often referred to as the base.

To calculate the perimeter of an isosceles triangle, you just need to know the length of one leg and the base.

Rule

The length of two sides are equal in an isosceles triangle.

Two angles are equal.

$$P=2\cdot \text{leg}+\text{base}$$ |

Example 2

The perimeter of this isosceles triangle is

$$P=2\cdot 5\phantom{\rule{0.17em}{0ex}}\text{cm}+3\phantom{\rule{0.17em}{0ex}}\text{cm}=13\phantom{\rule{0.17em}{0ex}}\text{cm}$$ |

A right triangle is a triangle where one angle is a right angle—an angle equal to $90$°. None of the sides of a right triangle must be the same length. That means in order to calculate the perimeter of a right triangle, you need to know the length of all its sides.

Rule

One angle of a right triangle is equal to $90$°.

$$P={\text{side}}_{1}+{\text{side}}_{2}+{\text{side}}_{3}$$ |

Example 3

The perimeter of this right triangle is

$$P=3\phantom{\rule{0.17em}{0ex}}\text{cm}+4\phantom{\rule{0.17em}{0ex}}\text{cm}+5\phantom{\rule{0.17em}{0ex}}\text{cm}=12\phantom{\rule{0.17em}{0ex}}\text{cm}$$ |

Finding the perimeter is often a simple procedure. If you don’t remember all the formulas in the boxes, you can always find the circumference by adding all the sides of the figure. This method of summation isn’t limited to only triangles, but all polygons with only straight sides.

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