Coincident triangle centers E

Area of equilateral triangle formula- definition ,concept

Formula

Area of equilateral triangle formula- definition ,concept

The area of an equilateral triangle is the amount of space that it occupies in a 2-dimensional plane.

To recall, an equilateral triangle is a triangle in which all the sides are equal and the measure of all the internal angles is 60°

.So, an equilateral triangle’s area can be calculated if the length of its side is known.

Area of equilateral triangle formula- definition ,concept
Area of equilateral triangle formula- definition ,concept

Derivation for Area of Equilateral Triangle

There are three methods to derive the formula for the area of equilateral triangles. They are:

  • Using basic triangle formula Using rectangle construction Using trigonometry

Deriving Area of Equilateral Triangle Using Basic Triangle Formula

Take an equilateral triangle of the side “a” units. Then draw a perpendicular bisector to the base of height “h”. in the equilateral triangle.

Area of equilateral triangle formula- definition ,concept
Area of equilateral triangle formula- definition ,concept

There are mainly three types of triangles which are scalene triangles, equilateral triangles and isosceles triangles .An equilateral triangle has all the three sides equal and all angles equal to 60°

. All the angles in an equilateral triangle are congruent.

Properties of Equilateral Triangle

An equilateral triangle is the one in which all three sides are equal. It is a special case of the isosceles triangle where the third side is also equal. In an equilateral triangle.

An equilateral triangle is a triangle in which all three sides are Equilateral triangles also called equiangular That means, all three internal angles are equal to each other and the only value possible is 60° each

Derivation for Area of Equilateral Triangle

  1. The area of an equilateral triangle is basically and the amount of space occupied by an equilateral triangle.
  2. In an equilateral triangle, the median, angle bisector and perpendicular .

Example Questions Using the Equilateral Triangle Area Formula

Question 1Find the area of an equilateral triangle whose perimeter is 12 cm.

Solution:

Given: Perimeter of an equilateral triangle = 12 cm

As per formula: Perimeter of the equilateral triangle = 3a, where “a” is the side of the equilateral triangle.

Step 1: Find the side of an equilateral triangle using perimeter.

3a = 12

a = 4

Thus, the length of side is 4 c

Therefore, the area of the given equilateral triangle is 4√3 cm2

Question 2What is the area of an equilateral triangle whose side is 8 cm?

Solution:

The area of the equilateral triangle = √3 a

= 16 √3 cm2

Question 3: Find the area of an equilateral triangle whose side is 7 cm.

Solution:

Given,

Side of the equilateral triangle = a = 7 cm

Area of an equilateral triangle = √3 a

= 21.21762 cm2

Q

 

 

Frequently Asked Questions

What is an Equilateral Triangle?

An equilateral triangle can be defined as a special type of triangle .

What is an equilateral triangle?

A triangle that has all its sides equal in dimension and each angle measure up to 60 degrees, is called an equilateral triangle.

An equilateral triangle is a regular polygon or a regular triangle.

What is the different name of triangles.

Based on sides, there are three different kinds of triangles. Their names are :Scalene triangle
Isosceles triangle Equilateral triangle
What is the perimeter of equilateral triangle with side equal to 10cm?
Perimeter = 3 x sides of equilateral triangle

Coincident triangle centers

Every triangle center of an equilateral triangle coincides with its centroid

, which implies that the equilateral triangle is the only triangle  connecting some of the centers and for some pairs of triangle centers,

The fact that they coincide is enough to ensure that the triangle is equilateral. In particular:

  • A triangle is equilateral if any two of the  centroid, or orthocenter coincide.

Six triangles formed by partitioning by the medians

For any triangle, the three medians partition the triangle into six smaller triangles.

  • A triangle is equilateral if and only if any three of the smaller triangles have either the same perimeter or the same in radius and  triangle is equilateral
  • if and only if the circumcenter of any three of the smaller triangles have the same distance from the centroid.

Area of Equilateral Triangle Using Trigonometry

If two sides of a triangle are given, then the height can be calculated using trigonometric functions. Now, the height of a triangle ABC will be-

h

Below is a brief recall about equilateral triangles:

What is an Equilateral Triangle?

There are mainly three types of triangles which are scalene triangles,

equilateral triangles and isosceles triangles. An equilateral triangle has all the three sides equal and all angles equal to 60

°. All the angles in an equilateral triangle are congruent.

Properties of Equilateral Triangle

An equilateral triangle is the one in which all three sides are equal. It is a special case of the isosceles triangle where the third side is also equal. In an equilateral triangle ABC, AB = BC = CA.

Some important properties of an equilateral triangle are:

  • An equilateral triangle is a triangle in which all three sides are equal.
  • Equilateral triangles also called equiangular. That means, all three internal angles are equal to each other and the only value possible is 60° each.
  • It is a regular polygon with  three sides.
  • A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid.
  • A triangle is equilateral if and only if any three of the smaller triangles have either the same perimeter.
  • The area of an equilateral triangle is basically the amount of space occupied by an equilateral triangle.
  • In an equilateral triangle, the median, angle bisector and perpendicular are all the same and can be simply termed as the perpendicular bisector .

 

Summary
Area of equilateral triangle formula- definition ,concept  The area of an equilateral triangle is the amount of spac
Article Name
Area of equilateral triangle formula- definition ,concept The area of an equilateral triangle is the amount of spac
Description
equilateral triangle is a triangle that has all its sides equal in length. For example, a triangle with its three sides equal to 5cm is an equilateral triangle. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees.
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