A scalene triangle is one of the three types of triangles which is classified based on their sides. The other triangles based on their sides are the isosceles triangle and equilateral triangle. A scalene triangleis a triangle that has all its sides of different lengths. It means all the sides of a scalene triangle are unequal and all the three angles are also of different measures. However, the sum of all the interior angles is always equal to 180 degrees. Thus, it meets the angle sum property condition of the triangle.
Some of the important properties of the scalene triangle are as follows:
It has no equal sides.
It has no equal angles.
It has no line of symmetry.
It has no point symmetry.
The angles inside this triangle can be acute, obtuse, or right angle.
If all the angles of the triangle are less than 90 degrees(acute), then the center of the circumscribing circle will lie inside a triangle.
In a scalene obtuse triangle, the circumcenter will lie outside the triangle.
A scalene triangle can be an obtuse-angled, acute-angled, or right-angled triangle.
Let's look into the Scalene Triangle Formula in detail.
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We will be learning about the following scalene triangle formula as listed below:
Area of a Scalene Triangle
Perimeter of a Scalene Triangle
Formula to Calculate the Area of a Scalene Triangle
The formula of the area of the scalene triangle is used to find the area occupied by the scalene triangle within its boundary.
The area of the scalene triangle is obtained by taking half of the product of the base to the height of the triangle. Thus, the formula for the area of the scalene triangle, with a base "b" and height "h" is "1/2 bh".
Area of a Scalene Triangle = (1/2 × base × height) square units
As the triangle has 6 quantities namely 3 sides and 3 angles, the area of a triangle is calculated via various formulas depending upon the known quantities of the triangle.
Area of a triangle with base and height
When the base and height of the scalene triangle is known, then the area of a triangle is:
Area of a triangle = 1/2 × (Base(b) × Height(h))
where b and h are the base and height of the triangle respectively.
Area of Triangle Using Heron's Formula
Heron's formula is applicable when all three sides of the triangle are known to us.
Consider the triangle ABC with sides a, b, and c has shown in the image.