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Equilateral Triangle Calculator

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:

Equilateral Triangle

 

  • 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:

$$ Area = \frac{1}{2} Base * Height $$
Equilateral Triangle Formula For Area

Case 2:

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

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

Case 2

How to Find the Height of an Equilateral Triangle?

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

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

How to Find the Height of an Equilateral Triangle

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