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Equilateral Triangle Calculator

This page provides some insight into equilateral triangles! Not only is it an equilateral triangle height calculator, it is also an area of equilateral triangle calculator, and can too find the perimeter of an equilateral triangle!

Calculation

Inputs



s
:5m​


Output



A
:10.8253175m2​



h
:4.33012702m​



P
:15m​


Explanation

An equilateral triangle is one in which all three sides have the same length and internal angle.
To find the area of an equilateral triangle, the below formula is used:

Area=3a24Area = \frac{\sqrt{3}a^2}{4}
The height of an equilateral triangle is given by:

Height=3a2Height = \frac{\sqrt{3}a}{2}
equilateral triangle calculation


The perimeter of an equilateral triangle is given by:

Perimeter=3aPerimeter = 3a

✍️ Algebraic proof

Using Pythagorean Theorem

Using Trigonometry

The triangle area formula using trigonometry

Area=12∗a∗b∗sin(γ)Area = \frac{1}{2} * a * b * sin(γ)
where γ is the angle between the sides.


Since all the sides and angles are equal in an equilateral triangle,

Area=12∗a∗a∗sin(60°)Area = \frac{1}{2} * a * a * sin(60°)

sin(60°)=32sin(60°) = \frac{\sqrt{3}}{2}
o now, the area of the equilateral triangle becomes

Area=12∗a2∗32=3a24Area = \frac{1}{2} * a^2* \frac{\sqrt{3}}{2} = \frac{\sqrt{3}a^2}{4}
angle between side of the triangle

60 degree angle between side of the triangle


The sine definition is used to determine the height of an equilateral triangle. The height of the equilateral comes from the sine definition:

ha=sin(60°) \frac{h}{a} = sin(60°) 

 h=a∗sin(60°)=a∗32 h = a * sin(60°) = a * \frac{\sqrt3}{2}

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