Question

Find the area of an equilateral triangle the length of whose one side is ‘a’​

Answer 1

Given :

⠀⠀⠀⠀⠀⠀⠀⠀ • Length of one side of an equilateral triangle is 'a'.

Construction :

⠀⠀⠀⠀⠀⠀⠀⠀• Draw a perpendicular bisector to the base of height 'h'.(see in fig. in attachment)

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)

⇒ A = (√3/4)a²

Answer 2

Answer:

√3 a^2 / 4

Step-by-step explanation:

Given,

side = a units

Area of an equilateral triangle = √3 a^2 / 4