Last modified on April 22nd, 2021

chapter outline

 

Equilateral Triangle

Definition

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

Equilateral Triangle

Properties

Properties of an Equilateral Triangle

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:

Area of an Equilateral Triangle

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    
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

Last modified on April 22nd, 2021

Leave a Reply

Your email address will not be published. Required fields are marked *