Equilateral Triangle Definition

In Geometry, different types of triangles are discussed depending on the lengths of the sides and the difference between angles. An equilateral triangle is a specific type of triangle that has all three sides and angles of equal measure.

Note:

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A triangle will be termed an equilateral triangle if it fulfills the following requirements.

  • All sides have the same lengths.
  • All angles are of the same measure.

Any triangle that is not fulfilling these requirements, will not be called an equilateral triangle. Because of the same lengths and angles, it is also called a Regular Polygon.

Note:

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Other types of Triangles

As mentioned above, you will see different types of triangles depending on the measures of the lengths. Here are the other two types of triangles depending on these factors.

  • Isosceles Triangle: It is a particular type of triangle that has 2 sides with equal measurements. In Isosceles Triangle, the measures of opposite angles will also same.
  • Scalene Triangle: In this type of triangle, all sides have different lengths and angles. It means no sides and angles are the same in Scalene Triangle.

Formulas related to Equilateral Triangle

Like other figures in Geometry, Equilateral Triangle also has different formulas to find the solution of this type of triangle. Here is the list of those formulas with a description.

Area Measurement

You can find the area of an equilateral triangle if you know the length of its side. Here is the formula that you need to apply for finding the area.

Area = √3a2/4

Here, “a” represents the length of any side of an equilateral triangle.

Example 1:

Find the Area of an equilateral triangle with sides of lengths 3 cm.

Solution:

To find the area of the triangle, you only need to follow the above formula.

Area = √3a2/4
= √3   〖(3)〗^2/4
= 3.9 square cm

Perimeter Measurement

To find the Perimeter of an equilateral triangle, you can only need to follow the following formula.

Perimeter = 3a

Here, “a” represents the sides of the triangle.

Example 2:

Find the Perimeter of an equilateral triangle having 5 meters as the length of its side.

Solution:

Here is the formula to find the Perimeter and the solution.

Perimeter = 3 (5)
= 15 meter

Fun Facts about Equilateral Triangle

  • All sides and angles of an equilateral triangle are the same.
  • The sum of all internal angles in this triangle is 180 degrees.
  • An equilateral triangle has an ortho-center and centroid at the same point.
  • The perpendicular drawn from a vertex on the opposite side will divide the triangle into two equal parts.

FAQ's

Is an equilateral triangle a polygon?

Yes, an equilateral triangle is also called a polygon.

Is an equilateral triangle a regular polygon?

An equilateral triangle is also called a regular polygon because it has sided with the same lengths and angles with the same measures.

What are the names of other types of triangles?

The other two types of triangles are called:

  • Isosceles Triangle
  • Scalene Triangle.

How do you know if a triangle is equilateral or not?

If a triangle has all three sides and angles of equal measure, it will be termed an equilateral triangle.

Can a right triangle be an equilateral triangle?

No, a right triangle can’t be an equilateral triangle because it has one angle of 90 degrees which makes the other two angles different from it.

What is the angle in an equilateral triangle?

The total angle in an equilateral triangle is 180 degrees.

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