Equilateral Triangle

If we go by what geometry says, an equilateral triangle is a triangle with all three sides equal in size. An equilateral triangle is also known as a regular polygon with three equal sides. In the following article, we’ll learn about the area of an equilateral triangle, its properties, and other formulas as well. If we break the term equilateral, we get ‘equi’, which means equivalent, and ‘lateral’ indicate the three sides of it.

What is an Equilateral Triangle?

If we see a triangle whose all three sides are equal in size, and its angles are equal as well, then it is known as an equilateral triangle. Every angle of the triangle is equal to 60 degrees; hence it can also be called an equiangular triangle.

A triangle can be categorized based on its sides and angles. They are isosceles triangle, equilateral triangle, and scalene triangle:

  • In a scalene triangle, all the three sides are different from each other, the angles are different from each other as well.
  • In the isosceles triangle, two sides are equal in size and the angles formed opposite of the equal sides are equal as well.
  • In the case of an equilateral triangle, as the name suggests, all the sides are equal in measure, and the angles are the same as well.

Properties of an Equilateral Triangle

Certain properties make an equilateral triangle unique from the rest and define the triangle as an equilateral. 

  • All three sides of an equilateral triangle are equal in size.
  • All the three angles formed inside the triangle are equal in measure and equivalent to 60 degrees.
  • It is also known as a regular polygon because of its equal sides.
  • The perpendicular which is drawn from any vertex of the triangle to the opposite side bisects the side in two equal lengths. The vertex is also equally divided into 30 degrees each.
  • In the equilateral triangle, median, altitude, and the angle bisector for every side are the same.
  • The sum of all the angles of the triangle must be 180 degrees.

Area of an Equilateral Triangle Formula

The formula that is used to calculate the area of an equilateral triangle is,

Area of an equilateral triangle = √3a2/4, given that a=side of the equilateral triangle.

Perimeter of an Equilateral Triangle Formula

The sum of all the three sides of an equilateral triangle is the perimeter of the triangle. Since all the three sides are equal, so the formula to calculate the perimeter can be written as,

The perimeter of an equilateral triangle = 3a, given that a is the side of the triangle.

  • The semi perimeter of an equilateral triangle=3a/2
  • The height of an equilateral triangle = √3a/ 2

How to Calculate the Area of an Equilateral Triangle

The steps describe the way to calculate the area of an equilateral triangle:

  • Step 1- Measure the length of one of the sides of the equilateral triangle.
  • Step 2- If a= the side of the triangle, then put the measurement and apply the formula, √3a2/4 to find out the value.
  • Step 3- Write the answer followed by the required unit.

Area of a triangle

The space occupied within the three sides of a triangle is known as the area of a triangle. The area of every triangle varies from the others based on its sides’ length and the angles formed. If we know the length of all three sides, then Heron’s formula is used, whereas, if we know the value of the two sides and the angle formed between them, we can use trigonometric functions to find the area out. However, the basic formula to calculate the area of a triangle is,

Area of the triangle = 1/2×base×height

The area of the triangle is expressed in the following square units and they are, m2, cm2, in2, etc.

To know more about the area of an equilateral triangle, visit Cuemath.

 

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