Question

the height of an equilateral triangle is 6 cm find the area of triangle under root 3 is equal to 1.732 ​

Answer 1

ANSWER:-

Given:

The height of an equilateral ∆ is 6cm.

To find:

Find the area of ∆.

Solution:

Let the side of an equilateral ∆ be 'x' cm.

We know that the area of an equilateral ∆;

$= > \frac{ \sqrt{3} }{4} ( {x)}^{2} ............(1)$

&

Area of ∆,

$= > \frac{1}{2} \times base \times heigh t\\ \\ = > \frac{1}{2} \times x \times 6 \\ \\ = > 3x {cm}^{2} .............(2)$

Now,

On equating (1) & (2), we get;

$= > \frac{ \sqrt{3} }{4} ( {x)}^{2} = 3x \\ \\ = > \frac{ \sqrt{3} }{4}x = 3 \\ \\ = > \sqrt{3} x = 12 \\ \\ = > x = \frac{12}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = > \frac{12 \sqrt{3} }{3} \\ \\ = > x = 4 \sqrt{3} cm$

Therefore,

Area of an equilateral ∆,

$= > \frac{ \sqrt{3} }{4} ( {x)}^{2} \\ \\ = > \frac{ \sqrt{3} }{4} ( {4 \sqrt{3)} }^{2} \\ \\ = > \frac{ \sqrt{3} }{4} \times 48 \\ \\ = > 12 \sqrt{3} {cm}^{2}$

=) (12 × 1.732)cm²

=) 20.784cm²

Hence,

The area of triangle is 20.784cm².

Hope it helps ☺️