An equilateral triangle is a geometrical figure, all three sides of which are equal in length. In this specific triangle, all three angles are also of equal measurements i.e. 60 degrees each. Since all three angles are equal, an equilateral triangle is also called an equiangular triangle. Let’s learn more about the basic concepts and area of equilateral triangle including its definition, formulas (perimeter, height), and properties.
What is an equilateral triangle?
In geometry, a triangle is said to be an equilateral triangle when all three sides and angles are equal to each other. Equilateral is composed of two words ‘equi’ which means equal and ‘lateral’ which means sides. An equilateral can also be referred to as a regular polygon having all three equal sides. The measurement of each angle in the equilateral angle is 60 degrees and thus, is also known as an equiangular triangle.
The mathematical formulas used to compute the area and perimeter of an equilateral triangle are as follows:
- Calculating the area of an equilateral triangle:
The area is referred to as the region which is covered by a geometrical figure. To compute the area of an equilateral triangle the following mathematical formula is used:
Area = √3a2/4
Here, ’a’ is the length of each three sides of an equilateral triangle.
- Calculating the perimeter of an equilateral triangle:
The perimeter of a geometrical figure refers to the length of all its sides. To compute the perimeter of an equilateral triangle, the length of all three sides is added.
Perimeter = 3a
- Calculating height of an equilateral triangle:
To compute the altitude or height of an equilateral triangle Pythagoras theorem can be used. We are very well aware of the fact that all three sides of an equilateral triangle are equal. When an altitude is drawn from the apex to the base of the triangle then the equilateral triangle gets divided into two equal right triangles.
Hence, the formula to compute the height of an equilateral triangle is:
Height = √3a/2
Properties of an equilateral triangle
There are some properties of an equilateral triangle defining a triangle as the equilateral triangle. The below-given properties will help one to identify a triangle as an equilateral triangle.
- All three sides in an equilateral triangle are equal in length.
- All three angles in an equilateral triangle are congruent and the measurement of each angle is equal to 60 degrees.
- An equilateral triangle can be called a regular polygon due to three sides being equal.
- When a perpendicular from any of the vertices to the opposite side of an equilateral triangle is drawn, it bisects the particular opposite side into two equal parts. Not only this but, the angle of the vertex from where the perpendicular is drawn is also bisected into two equal parts i.e. 30 degrees each.
- In an equilateral triangle, both the ortho-center and centroid are at the same point.
- Median, altitude, and angle bisector all three for the sides of an equilateral triangle are the same.
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