Introduction:-

In this article we are going to see about drawing of an equilateral triangle. Three intersecting lines form a closed figure is called a triangle. (‘Tri’ means ‘three’). As a triangle has three sides, it has three angles and three vertices. If the triangle having equal length in its all three sides then it’s called as equilateral triangle .The angles of an equilateral triangle are 600 each. "Equi" means that something same or equal; "lateral" refers to sides. These triangles are known as regular polygons and also equiangular in traditional Euclidean geometry.

**The properties of equilateral triangles:-**

Let the length of the side of the equilateral triangle ‘a’, we can decide that:

• The area of an equilateral triangle is A="a2(" v 3)/4

• The perimeter of an equilateral triangle is P="3a

• The radius of the circumscribed circle is R="a" (v 3)/3

• The radius of the inscribed circle is r="a(v" 3)/6

• The geometric center of the given triangle is the center of the circumscribed and inscribed circles

• The altitude or height of the equilateral triangle is h="a" (v 3)/2.

• Equilateral triangle is more symmetric.

• Equilateral triangle has three lines of reflection.

• Its rotational symmetry is order of 3.

• Equilateral triangle belongs to the symmetry group of dihedral group of order 6.

Example problems on Equilateral triangle:

Ex 1:- Find the area of the equilateral triangle of length 8cm.

Sol :- Let length = a="8" cm

The formula to find area of an equilateral triangle is A="(" v3/4) a2

A = (v3/4) * 82

= 0.433 * 64

A = 27.71200cm2

Ex 2:- The equilateral triangle having the length 5cm. Find its altitude.

Sol :- Let the length = a = 6cm.

Formula to find the altitude:

H= a (v 3/2)

= 5 (v 3/2)

= 5 * 0.866

Altitude = 4.33cm.

Ex 3:- Find the perimeter of an equilateral triangle whole length is 12 cm.

Sol :- Let length = a="12" cm

Perimeter = P="3a

= 3 * 12

= 36 cm.