Area Of Equilateral Triangle

Definition of Equilateral Triangle:

A triangle whose all three sides have the same length is termed as the equilateral triangle.

 

Area of an equilateral triangle:

    • Consider an equilateral triangle having sides equal to a.

Equilateral Triangle

    • We drop a straight line from the top vertex  to the midpoint of the base of the triangle, thus dividing the base into two equal halves.

Area Of Equilateral Triangle

  • Now we cut along the straight line and move the other half of triangle to form the rectangle.

Rectangle

We are considering the length of the equilateral triangle to be ‘a’ and let the height of it be ‘h’

So the area of an equilateral triangle = Area of a rectangle = \(\frac{1}{2}\times a \times h\) …………. (i)

The half of the rectangle is a right-angled triangle as it can be seen from the figure above.

Thereby applying the Pythagoras Theorem:

\(\Rightarrow (a)^{2} = (h)^{2}+ \left ( \frac{a}{2} \right )^{2}\)

\(\Rightarrow (h)^{2} = \left ( \frac{3}{4} \right )a^{2}\)

\(\Rightarrow h = \frac{\sqrt{3}}{2} a \) …………..(ii)

Substituting the value of (ii) in (i), we have:

Area of an Equilateral Triangle \(= \frac{1}{2} \times a \times \frac{\sqrt{3}}{2} a\)

\(= \frac{\sqrt{3}}{4} a^{2}\)<<>/p

This is all about the area of an equilateral triangle. To know more about the other characteristics of an equilateral triangle and other geometrical figures, please do visit www.byjus.com or download BYJU’S-The Learning App.’


Practise This Question

The cost of painting the whole surface area of a cube at the rate of 13 paise per cm2 is Rs 343.98. Then, the volume of the cube is