Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

Equilateral Triangle Calculator

Input the side, perimeter, area, circumcircle radius or altitude of an equilateral triangle, then choose a missing value.
The calculator will display step-by-step explanation on how to find the missing value.
show help ↓↓ examples ↓↓ tutorial ↓↓
The missing value:
Provide any value for an equilateral triangle.
Calculator works with decimals, fractions and square roots (to input $ \color{blue}{\sqrt{2}} $ type $\color{blue}{\text{r2}} $)
side
$ a = $
 
height
$ h = $
perimeter
$ P = $
 
area
$ A = $
circumcircle
radius
$ R = $
 
incircle radius
$ r = $
 
working...
Equilateral triangle formulas
$$ A = \frac{3 \, a^2 \sqrt{3}}{4} $$
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
example 1:ex 1:
What is the area of an equilateral triangle of perimeter $P = 6\sqrt{2}$.
example 2:ex 2:
What is the perimeter of an equilateral triangle if its height is $\dfrac{20}{3} cm^2$?
example 3:ex 3:
If base of an equilateral triangle 50 inches long, what is the triangle's height?
example 4:ex 4:
$\triangle ABC$ is an equilateral triangle with area A = 24. Find the perimeter.
TUTORIAL

Equilateral triangle calculations

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

Perimeter: $$ P = 3 \cdot a $$ equilateral triangle
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} $

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

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} $

$$ \begin{aligned} h & = \frac{a \sqrt{3}}{2} \\[ 1 em] 15 & = \frac{a \sqrt{3}}{2} \\[ 1 em] a \sqrt{3} & = 15 \cdot 2 \\[ 1 em] a \sqrt{3} & = 30 \\[1 em] a & = \frac{30}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\[1 em] a & = \frac{30 \sqrt{3}}{3} \\[ 1 em] a & = 10 \sqrt{3} \approx 17.3 \end{aligned} $$
Search our database of more than 200 calculators

Was this calculator helpful?

Yes No
437 782 151 solved problems