Area of Scalene Triangle - Formula, Examples, Definition

The space inside a scalene triangle between its borders makes up its entire area. A closed, two-dimensional plane shape having three sides and three angles is known as a triangle in geometry. There are three edges and three vertices on it. A scalene triangle is a particular kind of triangle in which the lengths of all three of the triangle's sides and the measures of its angles differ. It belongs to one of the three categories of triangles that may be identified by the characteristics of their sides. Even though a scalene triangle has several different angles, the total of all its internal angles is still 180 degrees. The area of a triangle is expressed in terms of the "number of" square units (square centimetres, square inches, square feet, etc.).

Properties Of A Scalene Triangle

• Possesses three uneven sides.

• Possesses no equal angles.

• Does not contain a symmetry point.

• It lacks one of the symmetry's sides, as it does not have equal sides.

• It can have acute, obtuse, or right-angled angles inside it.

• The term "acute angle" refers to any angle that is less than 90 degrees.

Types Of Scalene Triangles

The types of the scalene triangle are listed below:

• Acute-angled scalene triangle: When the triangle's circumcenter is within the triangle.

• Obtuse-angled scalene triangle: When the triangle's circumcenter is outside of it.

• Right-angled scalene triangle: When the hypotenuse's midpoint is the circumcenter.

Formulas For Calculating The Area Of A Scalene Triangle

Due to the triangle's six properties—its three sides and three angles—the area of a triangle can be determined using a variety of formulas depending on the triangle's properties. The base and altitude, the lengths of the three sides, or the lengths of any two sides and the angle between them can all be used to determine a scalene triangle's area.

• When the base and altitude of the scalene triangle are known.

Area = \frac{1}{2}\times Base\times Height

• When the lengths of all three sides of the scalene triangle are known, the area is computed using Heron's formula, that is,

Area = \sqrt{s(s-a)(s-b)(s-c)}

Here, a,b and c are the sides of the scalene triangle and ‘s’ is the semi-perimeter which is computed as, s=\frac{a+b+c}{2}

• When the length of the two sides of a scalene triangle and the angle between them is known.

Area = \frac{1}{2}\times a\times b\times \sin C

Here, a and b are the two sides of a scalene triangle and ‘C’ is the angle between these two sides.

The Perimeter Of A Scalene Triangle

A triangle's perimeter is equal to the sum of its side lengths and is represented as follows:

Perimeter = a + b +c

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

Points To Remember

• Three sides, each with a different length, and three angles, each with a different measurement, make up a scalene triangle.

• Additionally, it adheres to the triangle's angle sum property.

• A scalene triangle lacks symmetry because the lengths of the sides are unequal and even the angles have different measures.