Area of Equilateral Triangle: Overview, Properties, Examples

The area of equilateral triangle is the amount of space occupied by the triangle in a two-dimensional plane. We all know that an equilateral triangle is a triangle consisting of three equal sides and each of the three internal angles measuring 60 degrees. In an equilateral triangle, median, angle bisector and altitude are the same for all three sides.

Students learn the area of the equilateral triangle formula in order to solve mathematical problems. The area of an equilateral triangle can be calculated if the length of the sides is given. You can check NCERT Solutions for Class 9 Maths Chapter 7 (Triangles) for a better understanding of triangles and their types. We have provided detailed information on the area of the equilateral triangle in this article. Read on to find out the definition, properties, formula and examples.

Area of Equilateral Triangle: Definition

The area of equilateral triangle is the amount of space occupied by it in the two-dimensional plane. We all know that triangle is the simplest form of a regular polygon and the name ‘triangle’ derives from the fact that it has three angles formed by joining three line segments end to end. Basically, a triangle is a closed geometric shape that has three angles, three sides, and three vertices. The sum of the three angles of a triangle is 180°.

Triangles are classified based on the length of the sides and the measurement of angles. An equilateral triangle is one of the triangle types based on the length of the sides. This type of triangle has three equal sides. As a result, each angle of an equilateral triangle measures 60 degrees.

Area of Equilateral Triangle: Properties

Some of the important triangle properties are as under:

1. All sides of an equilateral triangle are equal.
2. All three internal angles are equal to each other.
3. It is a two-dimensional polygon.
4. The perimeter of an equilateral triangle is 3a.

Area of Equilateral Triangle: Formula

Below we have provided the formula for the area of equilateral triangle:

Where,
A is the area of equilateral
a is the length of the sides.

Area of Equilateral Triangle: Examples

Check the following examples on the area of equilateral triangle in order to have a clear idea about the concept:

Example 1: Find the area of an equilateral triangle with a side of length 7 cm?
Solution: Given, side of the equilateral triangle i.e. a = 8 cm

Arrea of an equilateral triangle,

A=  √3a²)/4

A=  √3 x 8²)/4

A= 64 x √3/4 sq.cm

A  = 27.7128 sq. cm

Thus area =   27.7128 sq. cm.

Example 2: Find the area of an equilateral triangle with a side of length 5 cm?
Solution: Given, side of the equilateral triangle i.e. a = 5 cm

Area of an equilateral triangle,

A=  √3a²)/4

A=  √3 x 5²)/4

A= 25 x √3/4 sq.cm

A  = 10. 8253 sq. cm

Thus, the area of equilateral triangle is 10.8253 sq. cm.

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Summary

The area of equilateral triangle can be defined as the amount of space occupied by it in the 2D plane. An equilateral triangle can also be described as the length of the sides. It is also important to note that all sides of an equilateral triangles are equal. Equilateral triangle is a regular polygon. The area of triangle can be calculated by using the formula A =√3a2)/4. The perimeter of an equilateral triangle is 3a.

FAQs on Area of Equilateral Triangle

Q.1. What is an equilateral triangle?
A. An equilateral triangle is a triangle with all three sides equal and all angles measuring 60 degrees.

Q.2. What is the area of an equilateral triangle?
A. The area of an equilateral triangle is the amount of space occupied by the triangle.

Q.3. What is the formula of area of an equilateral triangle?
A. The formula of area of an equilateral triangle is A =√3a²)/4.

Q.4. What type of polygon is an equilateral triangle?
A. Equilateral triangle is a regular polygon.

Q.5. State one property of Equilateral triangle.
A. One of the properties of an Equilateral triangle is described as all sides of an equilateral triangle are equal.

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