Question

Heya Mate


Prove that

Area of Equilateral Triangle =
$\frac{ \sqrt{3} }{4} \times (side) {}^{2}$
​

Answer 1

$\huge \bold \pink{answer - }$

Step 1: Since all the 3 sides of the triangle are same,

AB = BC = CA = a

Step 2: Find the altitude of the △ABC.  

Draw a perpendicular from point A to base BC, AD ⊥ BC

By using Pythagoras theorem

In △ ADC

h2 = AC2 - DC2

= a2 - (a2)2 [Because, DC = a2 ]

= a2 - a24

h = 3√a2

Step 3: We know that, Area of a triangle = 12 * Base * Height

= 12 * a * 3√a2

= 3√4a2

The area of a equilateral triangle = 3√4a2.

Answer 2

$\huge\color{red}\star\star{HELLO.}\star\star$

Since all the 3 sides of the triangle are same,

AB = BC = CA = a

Find the altitude of the △△ABC.

Draw a perpendicular from point A to base BC, AD ⊥⊥ BC

By using Pythagoras theorem

In △ ADC

h² = AC² - DC²

= a² - (a/2)² [Because, DC = a²]

= a²- a²/4

h = √3a/2

We know that, Area of a triangle = 1/2 * Base * Height

= 1/2 * a * 3√a/2

= √3/4*a²

The area of a equilateral triangle = √3/4*a²

hope it helped you !!^_^