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

Side length (s)

:5m

⬆️ Outputs

Area (A)

:10.8253175m2

Height (h)

:4.33012702m

Perimeter (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:

The height of an equilateral triangle is given by:

equilateral triangle calculation

The perimeter of an equilateral triangle is given by:

✍️ Algebraic proof

Using Pythagorean Theorem

The basic formula for triangle area is side b (base) times the height (h), divided by 2

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

equilateral triangle

Transforming the above-said equation to determine the height of an equilateral triangle:

Substituting h into the first area formula, we get

Using Trigonometry

The triangle area formula using trigonometry

where γ is the angle between the sides.

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

o now, the area of the equilateral triangle becomes

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:

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