What is an Equilateral Triangle?
An equilateral triangle, in geometry, is a triangle with three equal sides. Also the interior angles of an equilateral triangle are equal. As a result, each angle measures 60 degrees. Hence, it is sometimes referred to as an equiangular triangle. Equilateral triangles follow the same area, perimeter, and height formula as other types of triangles. Let’s read this article to discover more.
Properties of an Equilateral Triangle
- It is a regular polygon with three sides.
- The length of the three sides of an equilateral triangle are equal.
- All three angles between each sides are congruent and are equal to 60 degrees.
- When a perpendicular passing through the vertex of the triangle is constructed, it bisects the opposite side of the equilateral triangle.
- The ortho-center, incenter, circumcenter and the centroid of the equilateral triangle are at the same point.
- The median, angle bisector, and altitude for all the sides of an equilateral triangle are the same.
Area of an Equilateral Triangle Formula
The surface or region covered by an equilateral triangle is known as the area of an equilateral triangle.
Area of an equilateral triangle: \( A=\frac{\sqrt{3}}{4}a^2 \) square units.
Perimeter Formula of an Equilateral Triangle
The total measurement of the boundary covered by an equilateral triangle is known as the perimeter of an equilateral triangle. All sides of the equilateral triangle are congruent, so it is also a regular polygon of three sides. Therefore, the perimeter of the equilateral triangle will be three times the side length.
Let the side length of the equilateral triangle is ‘a’ units then,
Perimeter of an equilateral triangle, \( P = a + a + a = 3a \) units.
Rapid Recall
Solved Equilateral Triangle Examples
Example 1: One side of the equilateral triangle is given below. Determine the other angles and the side lengths of the equilateral triangle.
Solution:
Since the triangle given above is an equilateral triangle, all sides are equal, and each of the angles between the sides are equal to \( 60 \) degrees. So, the other two sides of the equilateral triangle are equal to 50 centimeters, and the other two angles are equal to \( 60 \) degrees.
Example 2: Determine whether the triangles provided below are equilateral triangles or not.
a.
b.
Solution:
Figure a
Since all sides of the triangle are equal in length, the triangle given here is an equilateral triangle.
Figure b
Since one of the sides is not equal to the other sides of the triangle, the triangle is not equilateral.
Example 3: An equilateral triangle is created using three sticks for a set of film props. The perimeter of the triangle is \( 456 \) cm. What would be the length of each side of the triangle?
Solution:
Since the triangle under consideration is an equilateral triangle, all of its sides will be equal. This means that we can obtain the length of each side by using the perimeter formula.
\( P = 3a \) Write the formula
\( 456 = 3a \) Substitute \( 456 \) for \( P \)
\( 152 = a \) Divide each side by \( 3 \)
Therefore, the length of the sides of the equilateral triangle is \( 152 \) centimeters.
All sides and angles of an equilateral triangle are equal.
An equilateral triangle is a regular polygon or a regular triangle.
On the basis of the side length, there are three different types of triangles.
- Scalene triangle
- Isosceles triangle
- Equilateral triangle
The centroid is a point of intersection of all three medians of a triangle.