A triangle having three equal sides which are congruent to each other is known as an Equilateral triangle. If we segregate the term equilateral into two parts; we will get equi + lateral where equi in Greek signifies equivalent or equal and lateral in Latin signifies sides, therefore equilateral triangle means equal sides. You might have observed various real-life objects such as traffic signs, monuments such as pyramids, all these are real-life examples of an equilateral triangle. In this article, we may try to cover some basic concepts related to an equilateral triangle such as the properties of an equilateral triangle, area of this triangle, and comparisons between various other triangles.
Some Important Properties of an Equilateral Triangle
A triangle having three equal sides which are congruent to each other can be defined as an equilateral triangle. The following points mentioned below analyses the significant properties of an equilateral triangle:
- In an equilateral triangle, all the three sides are equal, the angles are congruent to each other and most importantly the angles measure about 60 degrees respectively and in total the resultant value comes 180 degrees.
- An equilateral triangle can be defined as a polygon that is regular in shape having three edges or sides whose centroid and ortho-center originate and lie at the same point.
- The area of an equilateral triangle is given by √3a.a/4 where a is the side of the triangle and the perimeter of an equilateral triangle is 3a where a is also the sides of the triangle.
- When we talk about the median, altitude, angle bisector in an equilateral triangle, all of them are similar or exact in nature (size).
Area of an Equilateral Triangle
The area of an equilateral triangle can be defined as the space or the region that is occupied by the three equal sides of a triangle in a plane that is two-dimensional. If we represent the formula for the area of an equilateral triangle mathematically, it will seem like, √3a.a/4 where a = side of the triangle. Along with the area, we should also know the perimeter of an equilateral triangle; the perimeter can be defined as the resultant value that comes after the addition of three equal sides. Mathematically, perimeter is = 3a where a = sides of the triangle.
Examples Related to The Perimeter
Example 1:
Find the perimeter of the equilateral triangle if the sides are equal and congruent to each other having 3 cm.
Provided that,
AB = 3 cm
BC = 3 cm
CA = 3 cm
Using the formula for the perimeter of an equilateral triangle, 3a where a is the side,
3*3 = 9 cm
Thus, the perimeter of the triangle is 9 cm.
Example 2:
Find the perimeter of the equilateral triangle if the sides are equal and congruent to each other having 9 cm.
Provided that,
AB = 9 cm
BC = 9 cm
CA = 9 cm
Using the formula for the perimeter of an equilateral triangle, 3a where a is the side,
3*9 = 27 cm.
Thus, the perimeter of the triangle is 27 cm.
Equilateral Triangle Vs Isosceles Triangle
The following points analyses the differences:
- An equilateral triangle has three sides and angles which are equal whereas an isosceles triangle has two sides and angles which are equal.
- In an equilateral triangle, the origin of centroid and ortho-center are same and also lie on the same plane whereas in an isosceles triangle the origin of ortho-center and centroid is different.
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