Equilateral Triangle

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:

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) cm²
= 9√3 cm²

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