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# Equilateral Triangle Calculator

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The equilateral triangle calculator assists you in the calculation of the standard parameters of an equilateral triangle. The standard parameter can be the area, height, and perimeter.

## Equilateral Triangle:

The Equilateral Triangle is a special case of a triangle having all the slides equal to each and also the angles.

An equilateral triangle is also known as a regular triangle, there are certain properties an equilateral triangle has:

• The equilateral triangle has all the sides equal to each other.

Sides of Equilateral Triangle: a = b = c

• The equilateral triangle measurements of angles equal 60°, and these angles are congruent with each other.

$$m∠A = m∠B = m∠C = 60^\text{o}$$

• The altitude, the angle bisector, the perpendicular bisector, and the median of the equilateral triangle coincide with each other

### Equilateral Triangle Formula For Area:

The Equilateral triangle formula for Area can be derived by two following methods:

It depends on how you are going to find the area and what factors you have in the equilateral triangle equation.

#### Case 1:

Consider if you have the Base and Height of the  Equilateral triangle, then you can find the area by the given formula:

$$Area = \frac{1}{2} Base * Height$$

#### Case 2:

Consider you know the length of the sides of the Equilateral triangle, then use the equilateral triangle formula:

$$Area=\dfrac{\left(a^{2}*\sqrt{3}\right)}{4}$$

### How to Find the Height of an Equilateral Triangle?

You can calculate the height by the height of the equilateral triangle formula:

$$Height=\dfrac{\left(Side*\sqrt{3}\right)}{2}$$

### Equilateral Triangle Measurements For Perimeter:

The equilateral triangle equations for various measurements of the Perimeter are given below:

• The perimeter of Equilateral Triangle: P = 3a

The equilateral triangle formula for Semiperimeter:

• Semiperimeter of Equilateral Triangle: s = 3a / 2

#### Example 1:

Calculate height of equilateral triangle and its area whose side is 4cm.

Solution:

The length side  “a” = 4cm

We know that the area of the equilateral triangle is (√3/4)a2

Now, substitute the value a = 4 in the formula

A = (√3/4)42

A = √3 (4)

A = 1.732 (4)

A = 6.928 cm2

h = a × √3 / 2

h =  4 × √3 / 2

h =  4 × 0.866

h = 3.464 cm

Perimeter =  P = 3a

Perimeter =  P = 3(4)

Perimeter =  P = 12cm

Semiperimeter: s = 3a / 2

Semiperimeter: s = 12 / 2

Semiperimeter: s = 6 cm

You can measure the area, height, perimeter, and semi-perimeter with the equilateral triangle calculator.

### How to Use the Equilateral Triangle Calculator?

For various measurements possibilities, just follow the instructions given below:

Input:

• Select the parameters from the list
• Enter the required value of the parameter
• Hit the calculate Button

Output:

• The Side length
• The Area and Height
• The Perimeter and Semiperimeter

### References:

From the source of Wikipedia: Equilateral Triangle, Principal properties

From the source of study.com: Triangles, Angles