Question

the height of an equilateral triangle is 6 CM its area is

Answer 1

Let x be the side of triangle ABC

AD=6cm

AD⊥BC

DC=DB=x/2

By Pythagoras theorem

6²+x²/4=x²

36=x²-x²/4

36=3x²/4

3x²=36×4

x²=144/3

x²=48

x=4√3cm

area of triangle ABC=BC×AD/2

=4√3×6/2

=4√3×3

=12√3cm²

Answer 2

Answer:

Height of Equilateral triangle - 6cm

Area of the triangle = ?

$\begin{gathered}\underline{\sf\green{\bf{ Solution}}} \\\end{gathered}$

Let each side of the triangle be x cm.

Then,

Formula of height of Equilateral triangle;

$\begin{gathered}\implies {\sf{ ( \dfrac{ \sqrt{3} }{2} \times a ) cm }} \\ \\\end{gathered}$

After putting Values,

$\begin{gathered}\implies {\sf{ \dfrac{ \sqrt{3} }{2} \times a \: cm = 6cm }} \\ \\ \implies{\sf{ a = ( \dfrac{6 \times 2}{ \sqrt{3}} ) }} \\ \\ \implies{\sf{ s = 4 \sqrt{3} \: cm}} \\\end{gathered}$

$\begin{gathered}\bullet{\underline{\boxed{\sf\red{ Formula\:used:-}}}} \\\end{gathered}$

$\begin{gathered}\implies {\sf{ Area\:of\: Equilateral = ( \dfrac{ \sqrt{3}}{4} \times a^2 ) }} \\ \\ \implies {\sf{ \dfrac{ \sqrt{3}}{4} \times (4 \sqrt{3})^2 }} \\ \\ \implies{\sf{ \dfrac{ \sqrt{3}}{4} \times 48 }} \\ \\ \implies{\sf{ 12 \sqrt{ 3} cm^2 }} \\\end{gathered} </p><p>⟹AreaofEquilateral=$

Hence,✔

The area of the given Triangle is ${\sf{ 12 \sqrt{ 3} cm^2 }}$