Question

how to find area of an equilateral triangle where a is the length of the side​

Answer 1

Answer:

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

Step-by-step explanation:

ABC is a equilateral triangle.

Here, AB = BC = AC = a

Construction : draw AD Perpendicular BC.

Then, we get,

BD = DC = a/2

We have, two right angled triangle

In triangle ABD,

(Hypotenuse ) AB = a

BD = a/2

(height) AD = ?

By pythagoras theorem,

(AB) ² = (BD)² + (AD)²

(AB)² - (BD)² = (AD)²

(AD)² = a² - a²/4

(AD)² = (4a² - a²)/4

(AD)² = 3a²/4

AD = (root3 × a ) /2

Now, we have,

(Height of equilateral triangle) AD= (root3 × a ) /2

(base of equilateral triangle) BC = a

We know that,

. ' . Area of triangle = 1/2 × base × height

= 1/2 × BC × AD

= 1/2 × a × (root3 × a ) /2

= root3 a²/4

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