Question

derive the formula of an equilateral triangle with side 'a'

Answer 1

Answer:

Deriving Area of Equilateral Triangle Using Basic Triangle Formula

Take an equilateral triangle of the side “a” units. Then draw a perpendicular bisector to the base of height “h”.

Deriving Area Of Equilateral Triangle

Deriving Area Of Equilateral Triangle

Now,

Area of Triangle = ½ × base × height

Here, base = a, and height = h

Now, apply Pythagoras Theorem in the triangle.

a2 = h2 + (a/2)2

⇒ h2 = a2 – (a2/4)

⇒ h2 = (3a2)/4

Or, h = ½(√3a)

Now, put the value of “h” in the area of the triangle equation.

Area of Triangle = ½ × base × height

⇒ A = ½ × a × ½(√3a)

Or, Area of Equilateral Triangle = ¼(√3a2)

Step-by-step explanation:

HOPE IT HELPS

MARK BRAINLIEST