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Triangle Formula

In geometry, various shapes and structures are used for the study. Many polygons are also there. A triangle is defined as a basic polygon with three edges and three vertices. It is a very basic shape in geometry. The length of the sides, as well as all three angles, will have different values. Triangles are also divided into different types based on the measurement of its sides and angles. In this topic, we will discuss various triangles with triangle formula and suitable examples. Let us begin learning!

triangle formula

Triangle Formula

What is the triangle?

As we saw that triangle is a closed polygon with minimum numbers of sides i.e. three. It is the easiest polygon which works as the base for other polygons with more number of sides. This also represents the smallest stable closed shape. Two very basic rules for a triangle are:

  1. The sum total of all three angles will be \(180^{\circ}\)

\(If \angle A, \angle B, and \angle C are three angles in a \Delta ABC, then: \)

\(\angle A +  \angle B + \angle C = 180^{\circ} \)

  1. The sum of any two smaller sides will be always larger than the biggest side.

If the length of two smaller sides in \(\Delta\) ABC are a and b and the largest side length is c, then:  a+b> c

Types of Triangles

Triangles are of different types. Some of these are:

  1. Equilateral Triangles: The Equilateral Triangles have the following properties:
  • Three sides with equal length
  • Three angles all equal to \(60^{\circ} \)
  • Three lines of symmetry
  1. Isosceles Triangles: The Isosceles Triangles have the following properties:
  • Only two sides of equal length
  • Only two equal angles
  • One line of symmetry
  1. Scalene Triangles: Scalene triangles have the following properties
  • All sides of different equal lengths
  • All angles are different
  • No lines of symmetry
  1. Acute triangles: Acute triangles have all acute angles i.e. angles less than\( 90^{\circ}\)
  2. Right Triangles: The Right Triangles is having one right angle i.e. equal to \( 90^{\circ}\)
  3. Obtuse triangles: Obtuse triangles have one obtuse angle i.e. angle which is greater than \( 90^{\circ}\)

The Triangle Formula is given below as,

  1. The perimeter of a triangle:

P = a + b + c

Where

P Perimeter of triangle
a, b, c Length of three sides

 

  1. Area of a triangle:

A = \(\frac{b X h}{2} \)

Where,

A Area of triangle
b Length of base of the triangle
h Height of the triangle

 

  1. If only two sides and an internal angle is given then the remaining sides and angles can be easily computed by using the formula given below:

\( \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC} \)

 

\( \angle A, \angle B, and \angle C\) Angle measurements of the triangle
a, b, c Length of three sides

Solved Examples

Q.1: Find the area of a triangle with sides a = 4 cm, b = 7 cm, c =4  cm?

Solution:

Given,

a = 4 cm

b = 7 cm

C= 4 cm. So the given triangle is isosceles type.

As we already know that height of an isosceles triangle

h = \(\sqrt{s^2-(\frac{b}{2})^2} \)

= \( \sqrt{4^2-(\frac{7}{2})^2} \)

= \( \sqrt{16–\frac{49}{4}} \)

= 1.93 cm

Area of an isosceles triangle,

A = \(\frac{b X h}{2}\)

= \(\frac{7 X 1.93}{2}\)

= 6.77 square cm

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