What is a Triangle?
A polygon with three sides and three vertices is a triangle. In geometry, it is one of the fundamental topics of geometry. A triangle with vertices A, B, and C, is represented as △ ABC. In Euclidean geometry, any three non-collinear points determine a unique triangle and a unique plane at the same time. In a triangle, three angles are there. Each angle is formed when any two sides of the triangle meet at a common point, known as the vertex.
Perimeter of Triangle Formula
The perimeter of any polygon is the sum of the lengths of the edges.
In the triangle,
Perimeter = The sum of the three sides
Area of a Triangle
The triangle’s area is the total region that is enclosed by the three sides of any particular triangle. It is equal to half of the height of the basic periods. Therefore, we have to know the base and height of it to find the field of a tri-sided polygon.
Let us find out the area of different types of triangles.
In a triangle of isosceles, two sides are equal in length. Also equal to each other are the two angles opposite to the two equal sides.
In case base and height are given, we use the following formula:
A = ½ × height × base
If three sides are given :
A = ½[√(a2 − b2/4) × b]
Using 2 sides of the triangle and an angle between them :
A = ½ × b × c × sin(α)
Using two angles between two sides and their length :
A = [c2 × sin(β) × sin(α)/ 2 × sin(2π−α−β)]
A scalene triangle is a type of triangle in which there are different side dimensions on all three sides. The three angles are therefore different from each other due to this.
A = ½ × height × base
There are all three sides of an equilateral triangle equal to each other. As a consequence, all the inner angles are equal degrees, i.e. each angle is 60°.
A = (√3)/4 × side2
A is the area of the triangle.
a is the length of the triangle.
b is the base of the triangle.
c is the third side of the triangle.
h is the height of the triangle.
α and β are the angles between two sides.
Determine a triangle area with a base of 12cm and a height of 10cm.
Area of a triangle = ½ × height × base
= ½ × 12 × 10
= 6 × 10
= 60 cm2
Since a triangle is a three-sided polygon, therefore to find the perimeter of a triangle we have to find the sum of the three sides. Similarly to find the area of a triangle, we must first know about the lengths of the sides of the triangle.