Perimeter of an equilateral triangle

Equilateral triangle


For calculate the perimeter of an equilateral triangle we only have to multiply by three the length of one of its sides. This is because this type of triangles has all its sides equal and, therefore, so are all its angles (60º each).

Equilateral triangle formula

Therefore, to calculate the perimeter of an equilateral triangle we need to apply the following formula mathematics:

Perimeter = a + a + a + a = 3a

By example.Let's calculate the length of an equilateral triangle whose side a = 15 centimeters. Applying the previous operation, we have:

P = a + a + a = 15 + 15 + 15 + 15 = 45 centimeters.

If you wish, we also have at your disposal a calculator with which you can automatically obtain the perimeter of this geometric figure with three equal sides just by entering the length of one of them:

Height of an equilateral triangle

Perimeter of a triangle

For calculate the height of the equilateral triangle we have to make use of the Pythagorean theoremso that:

  • The hypotenuse will have length a, that is, the length of one of the sides.
  • The shortest leg will have a length of a/2, that is, half of one of the sides. This is because the height crosses the center of the equilateral triangle and divides the side in half.
  • The longest leg corresponds to the height of the equilateral triangle

How do we calculate the height of the equilateral triangle? With these data, we can go to the calculator that you will find in the link that we have put above these lines and you can easily calculate the height of this type of geometric figure with the three equal sides from Pythagoras.

If you prefer, you can apply the following mathematical formula which will give you a similar result, although you will have to do the calculation manually:

Height of equilateral triangle
Formula for calculating the height of an equilateral triangle

For example, let's calculate the height of the equilateral triangle that we have seen in the previous example and whose side measured 15 cm. To do this, we apply the above formula and we get that:

h = √3/2 x 15 = 12.99 centimeters.

As you can see, obtaining the height of such a triangle does not involve too much difficulty and you only need to remember the formula (or deduce it yourself from the Pythagorean Theorem) to solve the problem.

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