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! 
CalculationInputs﻿﻿s
:5m​
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Output﻿﻿A
:10.8253175m2​
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﻿﻿h
:4.33012702m​
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﻿﻿P
:15m​
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ExplanationAn 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:
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Area=3a24Area = \frac{\sqrt{3}a^2}{4}Area=43​a2​
The height of an equilateral triangle is given by:
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Height=3a2Height = \frac{\sqrt{3}a}{2}Height=23​a​
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equilateral triangle calculation
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The perimeter of an equilateral triangle is given by: 
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Perimeter=3aPerimeter = 3aPerimeter=3a
✍️ Algebraic proof
Using Pythagorean Theorem
The basic formula for triangle area is side b (base) times the height (h), divided by 2
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Area=12∗b∗hArea = \frac{1}{2}* b * hArea=21​∗b∗h
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 triangle side
The height of an equilateral triangle is derived by splitting the equilateral triangle into two right triangles. One leg of right triangle is equal to height (h) and the other side of the triangle is half the original side (s/2); therefore,  the hypotenuse
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s2=h2+(s2)2s^2 = h^2 + (\frac{s}{2})^2s2=h2+(2s​)2
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equilateral triangle
Transforming the above-said equation to determine the height of an equilateral triangle:
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h=s∗32h = s * \frac{\sqrt{3}}{2}h=s∗23​​
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Substituting h into the first area formula, we get
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Area of an equilateral triangle=3a24Area \space of \space an \space equilateral\space  triangle = \frac{\sqrt{3}a^2}{4}Area of an equilateral triangle=43​a2​
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Using Trigonometry
The triangle area formula using trigonometry
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Area=12∗a∗b∗sin(γ)Area = \frac{1}{2} * a * b * sin(γ)Area=21​∗a∗b∗sin(γ)
where γ is the angle between the sides. 
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Since all the sides and angles are equal in an equilateral triangle, 
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Area=12∗a∗a∗sin(60°)Area = \frac{1}{2} * a * a * sin(60°)Area=21​∗a∗a∗sin(60°)
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sin(60°)=32sin(60°) = \frac{\sqrt{3}}{2}sin(60°)=23​​
o now, the area of the equilateral triangle becomes
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Area=12∗a2∗32=3a24Area = \frac{1}{2} * a^2* \frac{\sqrt{3}}{2} = \frac{\sqrt{3}a^2}{4}Area=21​∗a2∗23​​=43​a2​
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 angle between side of the triangle
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60 degree angle between side of the triangle
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The sine definition is used to determine the height of an equilateral triangle. The height of the equilateral comes from the sine definition:
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ha=sin(60°) \frac{h}{a} = sin(60°) ah​=sin(60°) 
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 h=a∗sin(60°)=a∗32 h = a * sin(60°) = a * \frac{\sqrt3}{2} h=a∗sin(60°)=a∗23​​
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