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Equilateral Triangle
In geometry, a triangle with all equal sides is said to be an equilateral triangle. If we break the word equilateral, here "equi" refers to equivalent and "lateral" refers to sides. An equilateral triangle is also called a regular polygon with three sides equal. In this article, we will learn about the equilateral triangle, properties of equilateral triangle and formulas of an equilateral triangle.
1.  What is an Equilateral Triangle 
2.  Properties of Equilateral Triangle 
3.  Formulas of Equilateral Triangle 
4.  FAQs on Equilateral Triangle 
What is an Equilateral Triangle?
An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. The equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.
The triangles are categorized into three different types based on their sides. They are isosceles triangle, scalene triangle, and equilateral triangle. The equilateral triangle is different from the isosceles and scalene triangle.
 In the scalene triangle, all the sides of the triangle are not equal and angles are also not equal.
 In the isosceles triangle, two sides are equal and the opposite angles of equal sides are equal.
 In an equilateral triangle, all sides are equal and angles are also equal.
Look at the given figure
In the given figure the sides of triangle ABC are equal i.e.
AB=BC=CA = a units.
Also, ∠A, ∠B and, ∠C = 60°
Therefore, according to the definition of the equilateral triangle the triangle, ABC is an equilateral triangle.
Properties of Equilateral Triangle
An equilateral triangle has some properties which define a triangle as an equilateral triangle. Follow the below properties for the identification of an equilateral triangle.
 sides of an equilateral triangle are equal in measurements.
 angles are congruent of an equilateral triangle and are equal to 60 degrees.
 a regular polygon because it has three sides.
 the perpendicular drawn from any of the vertex to the opposite side of an equilateral triangle bisects the side in equal lengths. It also bisects the angle of the vertex into equal halves i.e. 30 degrees each from where the perpendicular is drawn.
 Orthocentre and centroid are at the same point.
 median, angle bisector and altitude of an equilateral triangle for all sides are the same.
 area of an equilateral triangle = √3a^{2}/ 4, here a = side of an equilateral triangle
 perimeter of an equilateral triangle = 3a, here a = side of an equilateral triangle
 The sum of all the angles of an equilateral triangle is equal to 180 degrees.
Equilateral Triangle Formulas
The formulas to find the area of an equilateral triangle and the perimeter of an equilateral triangle are mentioned below.
Area of an Equilateral Triangle
The area of an equilateral triangle is the space covered by the triangle in a twodimensional plane. The formula to find the area of an equilateral triangle is here:
Area of an equilateral triangle = √3a^{2}/ 4, where a is the side of an equilateral triangle.
Perimeter of an Equilateral Triangle
The sum of all sides of an equilateral triangle is the perimeter of an equilateral triangle or three times of a side because all sides are equal in an equilateral triangle.
The perimeter of an equilateral triangle = 3a, where a is the side
Also, note,
 Semi Perimeter of an Equilateral Triangle = 3a/2
 Height of an Equilateral Triangle = √3a/ 2
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Equilateral Triangle Examples

Example 1: Calculate the area of an equilateral triangle whose sides are 20 inches.
Solution: Area of equilateral triangle = √3a^{2} / 4, where a is the side
Given, a = 20 inches
Therefore, area = √3×20×20 / 4
Area of an equilateral triangle = 100√3 square inches 
Example 2: What is the perimeter of an equilateral triangle whose sides are 40 inches. Also, find the height of an equilateral triangle
Solution: Perimeter of an equilateral triangle = 3a, where a is the side
Given a = 40 inches
Perimeter of a equilateral triangle = 3 × 40 = 120 inches
Height of an equilateral triangle = √3a/ 2 = √3 × 40 / 2 = 20 √3 
Example 3: What are the perimeter and semi perimeter of an equilateral triangle with side measurement as 12 units.
Solution:
Perimeter of equilateral triangle = 3a and semiperimeter of an equilateral triangle = 3a/ 2, where a is the side. Given a = 12 units. Therefore, the perimeter of equilateral triangle = 3 × 12 = 36 units and Semiperimeter of an equilateral triangle = 36/2 = 18 units.
FAQs on Equilateral Triangle
What is an Equilateral Triangle in Geometry?
An equilateral triangle is a triangle in which all sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. An equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.
Is an Equilateral Triangle a Regular Polygon Why?
An equilateral triangle is considered as a regular polygon or a regular triangle as its angles and sides are equal.
What is the Sum of all the Angles of an Equilateral Triangle?
The sum of all the angles of an equilateral triangle is equal to 180 degrees. As all the angles are equal to 60 degrees, the sum is equal to 60°+ 60°+ 60° =180 degrees
What Are the Equilateral Triangle Formulas in Geometry?
In geometry, all the figures whether 2D or a 3D have certain specific formulas that are used to calculate the area, altitude, perimeter, and semiperimeter. Similarly, an equilateral triangle has the belowlisted formulas:
 Area of an equilateral triangle, A = (√3/4)a^{2}
 Perimeter of an equilateral triangle, P = 3a
 Semi perimeter of an equilateral triangle = 3a/2
 Height of an equilateral triangle, h = (√3a/2)
How to Find the Area of an Equilateral Triangle?
The area of an equilateral triangle can be found by using the formula of the area of an equilateral triangle. Area of an equilateral triangle = √3a^{2}/ 4, where a is the side of an equilateral triangle.
How Many Sides and Angles does an Equilateral Triangle have?
An equilateral triangle has three sides and three angles. The measurements of each side are the same and angles are equal to 60 degrees.
What is the Perimeter of The Equilateral Triangle with the side equal to 70 inches?
Perimeter of an equilateral triangle = 3 × sides of an equilateral triangle. Perimeter = 3 × 70 = 210 inches.
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