Question

findthe area of equilatteral tringlle with side 2root3 cm by use herons formula​

Answer 1

$\huge \green{ \mathfrak{solution}}$

Given:

side = 2√3cm

To find : Area of equilateral triangle by using Heron's formula .

Heron's formula :

$\boxed{\bold \red{{\sqrt{s(s - a)(s - b)(s - c)} }}}$

where S is semiperimeter =

$\boxed{ \blue{ \frac{a + b + c}{2} }}$

First find: S

All sides are same because it's an equilateral triangle

$\implies \: \frac{2 \sqrt{3} + 2 \sqrt{3} + 2 \sqrt{ 3} }{2} \\ \\ \implies \frac{6 \sqrt{3} }{2} \\ \\ \implies \: 3 \sqrt{3} cm$

Now ,

Area

$\rightarrow \: \sqrt{3 \sqrt{3} (3 \sqrt{3} - 2 \sqrt{3})(3 \sqrt{3} - 2 \sqrt{3} )(3 \sqrt{3} - 2 \sqrt{3} } \\ \\ \rightarrow \: \sqrt{3 \sqrt{3} ( \sqrt{3} )( \sqrt{3})( \sqrt{3} ) } \\ \\ \rightarrow \: \sqrt{3 \sqrt{3} (3 \sqrt{3} )} \\ \\ \rightarrow \: \sqrt{ {(3 \sqrt{3} })^{2} } \\ \\ \rightarrow \: 3 \sqrt{3}$

Hence the area is

$\red{\boxed{ \boxed{ \purple{ \: 3 \sqrt{3} {cm}^{2}} }}}$