Question

Solve question no. 18

Answer 1

Answer:

Height of equilateral triangle = 9cm

Height of equilateral triangle is given by formula = √3/2 * side²

So,

9 = √3/2 * side

side = (9*2)/√3

side = 3√3 * 2

side = 6√3 cm

Now Area of equilateral triangle is given by formula, = √3/2 * side²

Area = √3/2 * (6√3)²

area = √3/2 * 108

area = 54√3cm²

area = 54*1.732 cm²

= 93.53cm²

If you want to know how the formula of equilateral triangle has been proved, then comment.

Answer 2

$\large{\mathfrak{\underline{\underline{Answer :-}}}}$

Given :-

Height of equilateral triangle = 9 cm

To Find :-

Area of equilateral triangle

Solution :-

Using Formula :-

$\large{\star{\sf{\boxed{\boxed{{\frac{{\sqrt{3}}}{2}} {\times} {side} \: = \: Height}}}}}$

_____________[Put values]

⇒ √3/2 * Side = 9

⇒ √3 * Side = (9 * 2)

⇒ √3 * side = 18

⇒ Side = 18/√3

⇒ Side = 18 * √3 / √3 * √3

⇒ Side = 18√3 / (√3)²

⇒ Side = 18√3 / 3

⇒ Side = 6√3 cm

$\huge{\sf{\boxed{\boxed{Side \: = \: 6{\sqrt{3}}cm}}}}$

Using Formula :-

$\large{\sf{\star{\boxed{\boxed{{\frac{{\sqrt{3}}}{4}} {\times} {side^{2}} \: = \: Area}}}}}$

⇒ √3/4 * (6√3)²

⇒ √3/4 * 108

⇒ √3 * 27

_______________[Put value of √3]

⇒ 1.732 * 27

⇒ 1732 * 27/1000

⟹ 46764/1000

⟹ Area = 46.764 cm²

$\huge{\sf{\boxed{\boxed{Area \: = \: 46.764 cm^{2}}}}}$