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# Area of a scalene triangle‌

Based on the measure of sides, triangles are classified as equilateral triangles, scalene triangles and isosceles triangles. Based on the measure of its interior angles, there are three types of triangles namely, acute triangle, obtuse triangle and right triangle.

A scalene triangle is a 3-sided closed polygon. It has three sides of unequal length. No side is equal to the other in measurement. This also implies that all the angles present on the vertices of the triangle are unequal. Since the sides of a scalene triangle are different, the angles corresponding to the sides are also different. The angle opposite to the largest side is the largest of the three angles. Similarly, the angle opposite to the smallest side is also the smallest. For example,

ABC is a scalene triangle with all the sides different from each other.

AB ≠ BC ≠ CA

Also,

∠ABC ≠ ∠BCA ≠ ∠CAB

## Properties of a scalene triangle

A scalene triangle has the following properties:

1. All three sides of the triangle are of different lengths.
2. All the interior angles of the triangle are different in measure.
3. The side opposite to the largest angle is the largest of all sides and vice versa.
4. The side opposite to the smallest angle is the smallest side in the triangle.
5. A scalene triangle obeys the angle sum property of a triangle which means the sum of all the interior angles of a scalene triangle is 180°.
6. A scalene triangle can be acute-angled or obtuse-angled, either at a time.
7. A right-angled triangle can also be a scalene triangle.
8. A line of symmetry does not exist in a scalene triangle.

## Area of a scalene triangle

The area of a scalene triangle can be calculated by different methods as discussed below:

1. Method 1
If the measurement of the height and base of the triangle is given, then the area of the scalene triangle will be
Area = ½ . base . height
Area= ½ . b . h
Where b is the base of the scalene triangle and h is the height of the triangle.
2. Method 2
If the measure of base and height is not given then Heron’s formula can be used to calculate the area of a scalene triangle. When the measurements of the sides of a triangle are given, the area of the scalene triangle will be
Area = √{s . (s-a) . (s-b) . (s-c)}
Where ‘s’ is the semi perimeter of the scalene triangle calculated as
S = (a + b + c)/2
and a, b, c are the unequal sides of the scalene triangle.
3. Method 3
When the measure of two sides and an angle is given, the area of a scalene triangle can be obtained using the following formula
Area = ½ . side₁ . side₂ . sinθ
Where side1 and side2 are the given sides and θ is the given angle.
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