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Equilateral Triangle Calculator
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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 $ 24 $. Find the perimeter.
TUTORIAL
Equilateral triangle calculations
This calculator uses the following formulas to find the missing values of a triangle.
| Perimeter: | $$ P = 3 \cdot a $$ |  |
| 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
Please tell me how can I make this better.
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