Equilateral Triangle

Equilateral triangle is a triangle in which all the three sides and angles are equal. Equilateral triangle definition states that the triangles are equiangular. That is, all the three internal angles are also congruent to each other and also measure of each angles are 60⁰.

Equilateral triangle is a triangle in which all the three sides and angles are equal. Equilateral triangle definition states that the triangles are equiangular. That is, all the three internal angles are also congruent to each other and also measure of each angles are 60⁰.

In the above shown figure, all the angles and sides of the triangle are of equal measure. And, therefore, it is called as an equilateral triangle. Equilateral Triangle is also a regular polygon.Therefore, it can also be referred to as regular triangles. A regular tetrahedron is made up of four equilateral triangles.

We can assume the length of the sides of the equilateral triangle are ‘a’. From this, we can determine that:

• The area of the equilateral triangle is A = a²( √3)/4
• The perimeter of the equilateral triangle is P = 3a
• The radius of the circumscribed circle is

R = a ( √3)/3

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

• The geometric center of the given triangle is the center of the circumscribed and inscribed circles
• The altitude or height of equilateral triangle is h = a(√3)/2

Below are some examples based on equilateral traingle

Example 1: Find the area of the equilateral triangle with side length 5 cm.

Area = a² ( √3)/4

= 5²(1.732)/4

= 43.3/4

= 10.825cm²

Example 2: Find the Perimeter of the given equilateral triangle with the side length 10 cm.

Perimeter P = 3a

= 3 * 10

= 30 cm.

Example 3: An equilateral triangle has one side that measures 10 in. What is the size of the angle opposite that side?

Solution:

Step 1: Since it is an equilateral triangle all its angles are 60⁰. The size of the angle does not depending upon on the length of the side.

Answer: The size of the angle is 60⁰.