Question

the height of an equilateral triangle is9√3 find its area

Answer 1

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Given :

height of an equilateral triangle = $9\sqrt{3}$

we know that, height of an equilateral triangle = $\frac{ \sqrt{3} }{2} a$

therefore,

side of equilateral triangle = 18 cm.

area of equilateral triangle = $\frac{ \sqrt{3} }{4} {a}^{2}$


hence,
area of the equilateral triangle = $\frac{ \sqrt{3} }{4} \times 324$

= $81\sqrt{3}$


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Answer 2

Answer :

The area of equilateral triangle is 81√3.

Step-by-step explanation :

Given :

Height of an equilateral triangle = 9 √ 3.

We know that ;

Height of an equilateral triangle = (√3 / 2) a

⇒ √ 3 a / 2 = 9 √ 3

⇒ √ 3 a = 2 ( 9 √ 3 )

⇒ a = 18 √ 6 / √ 3

⇒ a = 9 × 2

⇒ a = 18

Now, area of an equilateral triangle = (√3 / 4)a²

⇒ Area = √3 / 4 × 18 × 18

⇒ Area = √3 × 9 × 9

⇒ Area = 81 √ 3

Hence, the area of equilateral triangle is 81√3.