Question

Perimeter of an equilateral triangle is 21.6sqcm.what is the area of it

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf{Given:-}\begin{cases}\sf{Perimeter\:of\: equilateral\:\triangle}\\ \sf{\implies 21.6cm}\end{cases}$

We have to find the area of equilateral triangle

First find the side of triangle

$\boxed{\dag{\sf{Perimeter\:of\:\triangle=Sum\:of\:all\:sides}}}$

Let the side of triangle be n

$\sf: \implies Perimeter=sum\:of\:all\:sides\\ \\ \sf\implies 21.6=n+n+n\\ \\ \sf\implies 21.6=3n\\ \\ \sf\implies n=\cancel{\dfrac{21.6}{3}}\\ \\ \sf\implies n= 7.2cm$

Now the Area

$\boxed{\sf{\dag{\:\:Area\:of\: equilateral\triangle=\dfrac{\sqrt{3}}{4}a{}^{2}}}}$

• Where a is the side of triangle

$\sf\implies Area=\dfrac{\sqrt{3}}{4}\times 7.2\times 7.2\\ \\ \sf\implies Area=\dfrac{\sqrt{3}}{4}\times 51.84\\ \\ \sf\implies Area=\dfrac{\sqrt{3}}{\cancel4}\times \cancel{51.84}\\ \\ \sf\implies Area= \sqrt{3}\times 12.96\\ \\ \sf\implies Area=12.96\sqrt{3}cm{}^{2}$

$\underline{\dag{\sf{\:\:Area\:of\: equilateral\triangle=12.96\sqrt{3}cm{}^{2}}}}$

Answer 2

$\huge\bold\green{Question}$

Perimeter of an equilateral triangle is 21.6sqcm

what is the area of it ___________ ?

$\huge\bold\green{Answer}$

The area of the equilateral triangle is 12.96 √3 cm³

____________________

According to the question We have to find the area of equilateral triangle

Lets find the side of the triangle

$\tt\green{Perimeter\:of\:\triangle=Sum\:of\:all\:sides}$

Let the side of triangle be “ x ”

$\begin{lgathered}\tt Perimeter=sum\:of\:all\:sides\\ \\ \tt 21.6=x+x+x\\ \\ \tt 21.6=3x\\ \\ \tt x=\cancel{\dfrac{21.6}{3}}\\ \\ \tt x= 7.2cm\end{lgathered}$

Now , we have to find out the are of triangle ∆

$\tt\green{\:\:Area\:of\: equilateral\triangle=\dfrac{\sqrt{3}}{4}a{}^{2}}$

Hence , “a” is the side of triangle :-

$\begin{lgathered}\tt Area=\dfrac{\sqrt{3}}{4}\times 7.2\times 7.2\\ \\ \tt Area=\dfrac{\sqrt{3}}{4}\times 51.84\\ \\ \tt Area=\dfrac{\sqrt{3}}{\cancel4}\times \cancel{51.84}\\ \\ \tt Area= \sqrt{3}\times 12.96\\ \\ \tt Area=12.96\sqrt{3}cm{}^{2}\end{lgathered}$

Hence the area of the equilateral triangle is 12.96 √3 cm³