## Definition

Equilateral triangle is a figure where all three sides and angles are equal

## Properties

1. All
three sides are equal; in
∆ABC, sides AB = BC = CA

2. All three angles are equal
(equiangular),

so ∠ABC = ∠BAC = ∠ACB = 60°

3. There are three lines of symmetry

4. The altitude, median, angular
bisector, and the perpendicular line are all same and together called the
perpendicular bisector, shown as AE

5. The orthocenter and centroid are the same point, represented as O

## Formulas

**Area **

The formula is given below:

**Problem:** Finding the area of an equilateral triangle when only **THREE** **SIDES** are known

**Find the area of the equilateral triangle whose side measures 6 cm.**

Solution:

As we know,

**A** = **√3/4 (****a****)²**

Here, *a* = 6 cm

Hence, *A* = √3/4

× (6 × 6) cm^{2}

= 9√3 cm^{2}

**Perimeter **^{}

We know, **Perimeter (****P****) = ****a****+ ****b**** +****c**, where *a*, *b*, *c* are the measures of three sides

Since in an equilateral triangle three sides are equal i.e., *a* = *b* = *c *Hence, **P**** =**** 3a**