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Equilateral Triangle Calculator

Equilateral Triangle Calculator

Input one element of an equilateral triangle, and the calculator will find the five unknown elements. The calculator will provide a step-by-step explanation on how to calculate missing elements.

Equilateral triangle calculator

Input the side, perimeter, area, circumcircle radius or altitude of an equilateral triangle, then choose a missing element.
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Solve for

Input one element of an equilateral triangle.

side

a =

height

h =

perimeter

P =

area

A =

circumcircle radius

R =

incircle radius

r =

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Equilateral triangle formulas

Equilateral triangle with sides, height and incircle radius.

$$ A = \frac{3 \, a^2 \sqrt{3}}{4} $$

area

$$ h = \frac{a \sqrt{3}}{2} $$

height

$$ r = \frac{a \sqrt{3}}{6} $$

incircle radius

$$ R = \frac{a \sqrt{3}}{3} $$

circumcircle radius

Examples

ex 1:

What is the area of an equilateral triangle of perimeter $P = 6\sqrt{2}$.

ex 2:

What is the perimeter of an equilateral triangle if its height is $\dfrac{20}{3} cm^2$?

ex 3:

If base of an equilateral triangle 50 inches long, what is the triangle's height?

ex 4:

$\triangle ABC$ is an equilateral triangle with area A = 24. Find the perimeter.

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Equilateral triangle calculations

This calculator uses the following formulas to find the missing values of a triangle.

Perimeter:	$$ P = 3 \cdot a $$
Area:	$$ A = \frac{a^2 \sqrt{3}}{4} $$
Height:	$$ h = \frac{a \sqrt{3}}{2} $$
Circumcircle radius:	$$ R = \frac{a \sqrt{3}}{3} $$
Incircle radius:	$$ r = \frac{a \sqrt{3}}{6} $$

Example 01 :

What is the area of an equilateral triangle whose side is $ 12 cm $.

Solution:

In this example we have $ a = 12 $.

To find the area we will use formula $A = \dfrac{a^2 \sqrt{3}}{4} $

$$ \begin{aligned} A & = \frac{a^2 \sqrt{3}}{4} \\[ 1 em] A & = \frac{12^2 \sqrt{3}}{4} \\[ 1 em] A & = \frac{144 \sqrt{3}}{4} \\[ 1 em] A & = 36 \sqrt{3} \end{aligned} $$

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Example 02 :

What is the side of an equilateral triangle whose height is 15 cm?

Solution:

In this example we have $ h = 15 $.

To find height we will use formula $h = \dfrac{a \sqrt{3}}{2} $

$$ \begin{aligned} h & = \frac{a \sqrt{3}}{2} \\[ 1 em] 15 & = \frac{a \sqrt{3}}{2} \\[ 1 em] a \sqrt{3} & = 15 \cdot 2 \\[ 1 em] a \sqrt{3} & = 30 \\[1 em] a & = \frac{30}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\[1 em] a & = \frac{30 \sqrt{3}}{3} \\[ 1 em] a & = 10 \sqrt{3} \approx 17.3 \end{aligned} $$

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