Scalene triangle


Before referring to the scalene triangle , it is important to know what a triangle itself is. The triangle is a polygon that has three different sides that are responsible for giving rise to three vertices and three internal angles. When we refer to a polygon we refer to a flat figure that is delimited by different segments . Among the different classes of polygons are triangles : polygons made up of three segments (sides). This is considered one of the simplest figures in the area of geometry and depending on its sides, it can be classified into different types.


What is the scalene triangle?

The scalene triangles are those triangles that have three different sides, each with a different length . In other words, we can say that its three sides are different .

  • Characteristics of the scalene triangle
  • Properties
  • Elements
  • Height
  • Area
  • Perimeter
  • Angles
  • Calculate the sides of a scalene triangle
  • How many equal sides does a scalene triangle have?
  • Examples

Characteristics of the scalene triangle

The main characteristics of scalene triangles are the following:

  • It is considered as a regular polygon that has three sides and because its sides are all different in size, but it can also be considered as a simple polygon because none of its points meet.
  • The three sides of the scalene triangle have different measurements .
  • They are triangles that house three interior angles which are also all different.
  • It is also considered as a convex polygon.
  • They are considered one of the most resistant geometric figures that exist in the area of ​​geometry.
  • This type of geometric figure is considered the preferred to be used by many builders and architects when any building is erected.
  • It is important to mention that the term scalene is also used in geometry with reference to scalene trapezoids that, like triangles of this type, present all of their sides with different measurements.
  • When the scalene triangle is contained in a spherical surface, it is known as a spherical triangle .
  • The scalene triangle is also known as the unequal triangle .


One of its most important properties are its sides since they have lengths of different measures, which is why in this type of triangle it will never be possible to show two angles that have the same measure.

When two of the sides of the scalene triangle are addends , the result that is obtained will always be greater than the length of the third side .


Scalene triangles have three different elements and these are known as the leg adjacent to the angle, the leg opposite the angle, and the hypotenuse . These three elements are always present in a triangle. In addition to these, we can mention the interior of the triangle which is the interior point of it, the exterior border that is constituted by the three sides of the triangle, the topological equivalence that says that any triangle will be equivalent to a simple closed curve. Topological equivalence.

The ceviana or line that passes through the vertex of the triangle, the median that is the segment of the line that goes from the vertex to the midpoint of the opposite side and the bisector and circumscribed circumference, are three other elements that make up a scalene triangle.

Finally, within the elements of the triangle, the internal and external bisectors, the length of the bisector and Steiner’s Theorem can also be mentioned.


The height can be calculated when a side (b) and the height (h) associated with that side are known.

Area = (bh) / 2

Where b is the base and h is the height.


The area of ​​a scalene triangle can be calculated using Heron’s formula if the measures of all its sides (a, b and c) are known.

Area = √ (s (sa) (sb) (sc))

Where a, b and c are the three sides of the triangle and s the semiperimeter:

s = (a + b + c) / 2


The perimeter of a scalene triangle that has three unequal sides can be found by adding the three sides.

Perimeter = a + b + c

Where a, b and c are the three sides of the triangle.


The angles that scalene triangles have are completely different and there can never be a triangle within this classification that has two sides of equal measure, they will always be different.

Calculate the sides of a scalene triangle

All the sides of the scalene triangle must be measured using different mathematical procedures , since without these measurements it would be impossible to determine its perimeter.

How many equal sides does a scalene triangle have?

Remember that scalene triangles do not have any of their sides of equal measure because if so, they would be another type of triangle. Related to the sides of the scalene triangle we find the perimeter.

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