Table of Contents
Introduction to Area of Scalene Triangle
A scalene triangle is a triangle that has no equal sides and no equal angles. The length of each side is different, and the angles are also different. This type of triangle is often used in math problems, because it is easy to create and to solve.
Properties of a Scalene Triangle
A scalene triangle has three unequal sides. The angles between the sides are also unequal. The longest side is called the base, and the other two sides are called the legs.
Types of Scalene Triangle
There are three types of scalene triangles: isosceles, equilateral, and right. An isosceles triangle has two sides of the same length. An equilateral triangle has all three sides of the same length. A right triangle has one right angle.
Types of Scalene Triangle
The scalene triangle also has types, those are given below:
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Acute-angled scalene triangle: when the circumcenter lies inside the triangle.
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Obtuse-angled scalene triangle: when the circumcenter lies outside the triangle.
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Right-angled scalene triangle: when the circumcenter is at the midpoint of the hypotenuse.
In this article, we will get to know about different types of ways through which we can measure the area of the scalene triangle. The area is the total amount of space it occupies. The area can be calculated by the base and altitude or by knowing the length of the three sides or by the length of any two sides and the angle between them.
First Method:-
The first method by which an area can be calculated is if we know its base and altitude.
The area of a scalene triangle is given as =1/2 × base × height (altitude) sq. units
=1/2 × b × h sq. units
Second Method:-
The second method by which area can be calculated is if the length of all three sides is given.
The area is calculated through Heron’s Formula i.e.= √s(s−a)(s−b)(s−c) sq.units.
Here, a, b and c; are the length of the sides of the given triangle and s is the semi-perimeter of the triangle i.e. (a+b+c)/2
Third Method:-
This method is used if we know the length of any two sides of a triangle and the angle between them.
Area of triangle= 1/2 × a × b × sinC sq units.
Here, a and b are the length of the two sides and c is the given angle between them. These methods are very important in the study of triangles and mostly all the questions are based on this research.
