The term equilateral can be split into two parts- equi and lateral. Equi means equivalent and lateral means side. So it can be simply said the triangle, which is comprised on three equal sides, is known as equilateral triangle. In the concept of Euclidean geometry, equilateral triangle is also considered as equiangular. The concept of equiangular depicts all the three intersection reflects an angle of 60 degree with the feature of congruency. Since the sum of all the angles of a triangle is 180 degrees therefore each angle in this case must be 60 degrees. This is also called as a regular triangle. It is referred to as a special case of an isosceles triangle that does not only have its two sides equal but all the three sides equal.  Some examples of central triangles that are actually formed of equilateral triangles are

There are 6 different types of triangles. On the basis of the sides the triangles can be classified as Scalene, Isosceles and Equilateral. On the basis of the angles of the triangle they can be classified as Acute, Obtuse and Right.

The term scalene means odd or uneven. Thus scalene triangles are those triangles that have its side of different measures. The interior angles of the triangle are also different.

The term isosceles means having equal legs. Thus isosceles triangles have two different sides of equal lengths. The interior angles that are opposite to the equal sides are also equal to each other.

As discussed in the above paragraph, equilateral triangle means the triangle that has three equal sides and angles.

Acute triangles are those triangles where all the angles of the triangle are less than 90 degrees, but the sum of all the angles should be 180 degree.

Obtuse triangles are those triangles where one of the three interior angles has a value greater than 90 degrees. The other two angles however remains less than 90 degrees as the sum total of all the angles should be 180 degrees.

A right angle triangle refers to the triangle where one of the interior angle is equal to the value of 90 degree. In this case the side opposite to the 90 degree angle should have the longest value and it is termed as the hypotenuse.

If we combine the different triangles we can get triangle like Right Isosceles Triangle. This is a combination of isosceles triangle and a right angled triangle. So this triangle will have one angle as 90 degree and two sides as equal. Therefore, it must also have two angles as equal and hence the value of the other two angles must be 45 degrees each.

The inradius of a triangle refers to the radius of the circle that can be made within the triangle that touches all the sides of the triangle internally. Inradius can be calculated by dividing the area by the semi-perimeter. If the sides of an equilateral triangle is “a”, then