Question

The height of an equilateral triangle is 9 cm. find its area.

Please no scam

I am giving 30 points for this question and will also mark the brainliest if no scam

please ​

Answer 1

Height = √3/2 (side)=9

⇒ side = 18/√3

Now,

Area = √3/4 (side)²

= √3/4 × 18/√3 × 18/√3

=3√3 ×9

=3×1.732×9

=5.196×9

=46.764cm²

Answer 2

Equilateral Triangle

An equilateral triangle is a triangle which has three sides of equal length. It has three vertices, three edges. All three angles of an equilateral triangle are equal to 60 degree.

Here in this question we've been given that, the height an equilateral triangle is 9 cm. And we've been asked to find out the area of equilateral triangle.

First we required to calculate the side of equilateral triangle. Formula to calculate height of an equilateral triangle is given as:

$\implies h = \dfrac{ \sqrt{3} }{2}a$

Where, $h$ is the height of equilateral triangle and $a$ is the side of equilateral triangle.

Substituting the available values in the formula, we get:

$\implies 9 = \dfrac{\sqrt{3} }{2}a \\ \\ \implies 9 \times 2 = \sqrt{3}a \\ \\ \implies 18 = \sqrt{3}a \\ \\ \implies a = \dfrac{18} {\sqrt{3} }$

Now, we got the value of side $a$ of equilateral triangle. Formula to calculate area of an equilateral triangle is given as:

$\implies Area = \dfrac{ \sqrt{3} }{4}a^2$

Substituting the available values in the formula, we get:

$\implies Area = \dfrac{ \sqrt{3} }{4} \times \bigg( \dfrac{18}{ \sqrt{3} } \bigg)^{2} \\ \\ \implies Area = \dfrac{ \cancel{\sqrt{3}}}{4} \times \dfrac{18}{ \cancel{\sqrt{3}}} \times \dfrac{18}{ \sqrt{3}} \\ \\ \implies Area = \cancel{\dfrac{18}{4}}\times \dfrac{18}{ \sqrt{3} } \\ \\ \implies Area =4.5 \times \dfrac{18}{ \sqrt{3} } \\ \\ \implies Area = \cancel{\dfrac{81}{ \sqrt{3} } } \\ \\ \implies \boxed{Area =46.76}$

Therefore, the area of an equilateral triangle is 46.76 cm².