Question

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

Answer 1

Answer:

• Height of Equilateral triangle - 6cm
• Area of the triangle = ?

$\underline{\sf\green{\bf{ Solution}}}$

Let each side of the triangle be x cm.

Then,

Formula of height of Equilateral triangle;

$\implies {\sf{ \left( \dfrac{ \sqrt{3} }{2} \times a \right) cm }}$

After putting Values,

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

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

$\implies {\sf{ Area\:of\: Equilateral = \left( \dfrac{ \sqrt{3}}{4} \times a^2 \right) }} \\ \\ \implies {\sf{ \dfrac{ \sqrt{3}}{4} \times (4 \sqrt{3})^2 }} \\ \\ \implies{\sf{ \dfrac{ \sqrt{3}}{4} \times 48 }} \\ \\ \implies{\sf{ 12 \sqrt{ 3} cm^2 }}$

Hence,

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

Answer 2

Question :-

the height of an equilateral triangle is 6 cm find its area ?

Answer :-

Given :-

it is given that the height of the equilateral triangle is 6 CM .

What to find here ?

here we have to find the area of the equilateral triangle .

How to find it ?

∆ first of all we have to find the height of the equilateral triangle .

∆ then we have to find the area of the equilateral triangle .

Solution ;

to find the height of the equilateral triangle ;

Formula to be used ;

$\frac{ \sqrt{3} }{2} \times x \: cm$

now putting the value ;

√3/2× x= 6cm

=> x= 6×2/√3

=> x= 12√3 cm

now to find the area of the equilateral triangle ;

formula to be used ;

$\frac{ \sqrt{3} }{4} \times {x}^{2}$

now putting the value ;

√3/4 × (4√3)^2

=> √3/4 ×48

=> 12√3 cm^2

hence the area of the equilateral triangle is 12 root 3 cm square .(12√3)cm^2