Question

The height of an equilateral triangle is √6 cm. find Its area​

Answer 1

Let side of equilateral TRAINGLE = a cm

$\begin{gathered}\color{red}h = \frac{ \sqrt{3} }{2} a \\ \\ </p><p>\color{blue} \sqrt{6} = \frac{ \sqrt{3} }{2} a \\ \\\color{red}\frac{ \sqrt{6} \times 2 }{ \sqrt{3} } = a \\ \\ \color{hotpink} \boxed{ a = > 2 \sqrt{2} cm } \\ \\ \color{red}area = \frac{ \sqrt{3} }{4} {a}^{2} \\ \\ \color{skyblue} area = \frac{ \sqrt{3} }{4} \times ( 2\sqrt{2} {)}^{2} \\ \\ \color{pink}area = > \frac{ \sqrt{3} }{4} \times 8cm \\ \\ \color{red} \boxed{area = > 2 \sqrt{3} c {m}^{2} }\end{gathered}$

Answer 2

Answer:

Let side of equilateral TRAINGLE = a cm

$\begin{gathered}\begin{gathered}\color{red}h = \frac{ \sqrt{3} }{2} a \\ \\ \color{blue} \sqrt{6} = \frac{ \sqrt{3} }{2} a \\ \\\color{red}\frac{ \sqrt{6} \times 2 }{ \sqrt{3} } = a \\ \\ \color{hotpink} \boxed{ a = > 2 \sqrt{2} cm } \\ \\ \color{red}area = \frac{ \sqrt{3} }{4} {a}^{2} \\ \\ \color{skyblue} area = \frac{ \sqrt{3} }{4} \times ( 2\sqrt{2} {)}^{2} \\ \\ \color{pink}area = > \frac{ \sqrt{3} }{4} \times 8cm \\ \\ \color{red} \boxed{area = > 2 \sqrt{3} c {m}^{2} }\end{gathered}\end{gathered} </p><p>$