Determine the properties of equilateral triangles with our online calculator. Online Equilateral Triangle Calculator.
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An equilateral triangle is a type of triangle characterized by three equal sides and three equal angles. In other words, all sides of an equilateral triangle have the same length, and all interior angles are congruent, each measuring 60 degrees. This geometric shape exhibits a high degree of symmetry and uniformity.
A = angle A, B = angle B, C = angle C
a = side a, b = side b, c = side c
K = area, P = perimeter, s = semiperimeter, h = altitude
For example, A side length is a = 4
To calculate P, use the following formula: 3a. When substituting a for its value, you get 3(4), which equals 12.
To calculate s, use the following formula: 3a/2. When substituting a and s for their values, you get 3(4)/2, which equals 6.
To calculate K, use the following formula: (1/4) * √3 * a2. When substituting a for its value, you get (1/4) * √3 * 42, which equals 6.9282.
To calculate h, use the following formula: (1/2) * √3 * a. When substituting a for its value, you get (1/2) * √3 * 4, which equals 3.4641.
Key Properties of an Equilateral Triangle
Let’s delve into the key properties that define an equilateral triangle:
1. Equal Side Lengths
The most distinguishing feature of an equilateral triangle is that all three sides are of equal length. This property sets it apart from other types of triangles where sides typically have varying lengths.
2. Congruent Angles
In an equilateral triangle, all three interior angles are congruent, each measuring 60 degrees. This uniformity in angle measurement contributes to the triangle’s symmetry.
3. Angle Bisectors
The angle bisectors of an equilateral triangle, which are the lines drawn from each vertex to the midpoint of the opposite side, are also congruent and intersect at the incenter, which is equidistant from all three sides.
4. Perpendicular Bisectors
The perpendicular bisectors of the sides of an equilateral triangle all coincide at a single point, known as the circumcenter, which is equidistant from the three vertices of the triangle.
5. Equal Altitudes
In an equilateral triangle, the altitudes drawn from each vertex to the opposite side are equal in length. This property is significant when calculating the area of the triangle.
I hope this Equilateral Triangle Calculator is very helpful for your math calculation.