How to find the perimeter of an equilateral triangle

25.07.2021 | Education

Finding the perimeter of an equilateral triangle means calculating the distance around the shape itself. The easiest way is to fold all sides. However, there are cases when only the height of a triangle or one side is known, what to do in such situations? The article will tell you how to quickly find the perimeter of a triangle under different conditions.

Equilateral triangle - what is it

Such a triangle has three congruent sides and three equal angles. Knowing the size of one of the sides, you can find the rest. Since a triangle has three proportionate sides, it automatically has three identical angles. They add up to 180º, which, according to their identity, should be divided by 3. This means that any angle of a triangle is 60º. It can be concluded that an equilateral triangle is an acute figure.

How to find the perimeter of an equilateral triangle

Since the sides of an equilateral triangle are congruent, the length of one side is required to calculate its perimeter. We can say that the simple formula for the perimeter of an equilateral figure is: P \u003d c + c + c, where c is the length of one of the sides.

Find out the perimeter of a triangle with congruent sides, if the size of one is 7 dm.
It is known from the condition that the side of the figure is 7 dm, i.e. the other sides are identical.
According to the formula, the perimeter of a triangle is: P \u003d c + c + c, P \u003d 7 + 7 + 7 \u003d 21 dm.

A simplified way to find the perimeter of an equilateral triangle

Of course, an easier way to find the boundaries of a triangle is to multiply the length of each side by three. The formula will be: P = 3 x a, where a is the length of the side.

Estimate the perimeter of an equilateral triangle with a given side of 7 inches.
Substitute the values according to the formula: P= 3 x a , P= 3 x 7
P = 21
The perimeter of a triangle is 21 inches.
When the sides of the triangle are originally given in centimeters, your answer must also be in centimeters. In the example shown, the sides are 7 inches long, so the correct perimeter would be 21 inches.

How to find the perimeter of an equilateral triangle using the height

The height of a triangle with equal sides is 7 cm, find the perimeter.
According to the condition h = 7 cm, following the formula:
P \u003d 2√3 x 7 \u003d 24.249 cm.

Online calculation of the perimeter of an equilateral triangle

There are several sites (for example, the Calculator reference portal or the 2mb educational portal) that will help you quickly calculate the perimeter of a triangle, you just need to enter its parameters.

How to find the perimeter of an equilateral triangle - reverse calculation

There are cases when the school needs to find the side of an equilateral triangle, when the condition specifies the perimeter of the figure. Apply what you have learned: P = 3 x c, so c = P: 3

Find the length of the side of an equilateral triangle when the perimeter is 24 cm.
Based on the formula: c \u003d P: 3, c \u003d 24: 3 \u003d 8 cm
The length of the sides of a given triangle is 8 cm.