Question

How do you calculate the perimeter of an equilateral triangle?

Answer 1

Hint:
The equilateral triangle is a triangle whose all sides are equal. The perimeter of any triangle can be calculated by adding all the sides of the triangle.

Complete step by step solution:
As the name equilateral triangle means a triangle whose all sides are equal in dimension and all angles are also equal. This is called an equilateral triangle. The internal angles of an equilateral triangle are $${60}^{\circ }$$
The following is the equilateral triangle:

Where
a= side of the triangle
h= height of the triangle
Now we know that the perimeter of a triangle is equal to the sum of all its three sides.
Therefore,
$P=AB+BC+CA$
For an equilateral triangle
$AB=BC=CA=a$
Therefore, perimeter
$$\begin{gathered} P=a+a+a \\ =3a \end{gathered}$$
This is the perimeter of an equilateral triangle.
If we divide the perimeter of an equilateral triangle by two it becomes a semi perimeter of an equilateral triangle. Therefore, the becomes semi perimeter of an equilateral triangle is
$$\begin{gathered} P^{\prime }={\displaystyle \frac{P}{2}} \\ ={\displaystyle \frac{3a}{2}} \end{gathered}$$

Additional information:
The other parameters of an equilateral triangle like area, height can be calculated by the following expressions:
The area of the equilateral triangle is given by the following formula:
$A={\displaystyle \frac{\sqrt{3}}{4}}{a}^2$
The height of an equilateral triangle is given by the following formula:
$h={\displaystyle \frac{\sqrt{3}}{2}}a$

Note:
1) The equilateral triangle has all sides equal.
2) The internal angles of an equilateral triangle are equals to ${60}^{\circ }$.
3) The perimeter of an equilateral triangle can be calculated by multiplying the side of the equilateral triangle with 3.