Last modified on April 22nd, 2021

chapter outline

 

Triangle

Definition

In geometry, a triangle is a plane figure that is enclosed by three line segments.

Triangle

Parts

  • Side
  • Angle
  • Vertex

Properties

Basic Properties of a Triangle
  1. The sum of all the angles of a triangle is equal to 180°
  2. The sum of the lengths of any two sides of a triangle is greater than the length of the third side
  3. The difference between any two sides of a triangle is less than the length of the third side
  4. An exterior angle of a triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of the triangle

Formulas

Area of a Triangle

It is the total space enclosed by the triangle. The formula is given below:

Area of a Triangle

Problem: Finding the area of a triangle when the BASE and HEIGHT are known

Find the area of a triangle whose base is 6 cm and height is 4 cm?

Solution:

As we know,
A= ½ (b × h)
= ½ (6 × 4) cm
= 12 cm2

Problem: Finding the area of a triangle when only SIDES are known

Find the area of a triangle whose three sides are 3 cm, 4 cm, and 5 cm.

Solution:

Here we will use the Heron’s formula,
A = √s(sa)(sb)(sc), where s = ½ (a+b+c)
In this triangle, s = ½ (3 cm + 4 cm+ 5 cm) = 6 cm
Since, A= √s(sa)(sb)(sc)
= √6(6-3)(6-4)(6-5)
= √36
= 6 cm2

Perimeter of a Triangle

It is the distance covered around the edges of a triangle or simply the length of the boundary covered. The formula is given below:

Perimeter of a Triangle

Find the perimeter of a triangle whose three sides are 4 cm, 6 cm, and 8 cm

Solution:

As we know,
P = a + b + c, where a, b, c are the measure of three sides
= 4 cm + 6 cm + 8 cm
= 18 cm

Types

Triangles are classified into two groups: based on sides, 1) scalene, 2) isosceles, and 3) equilateral triangles; based on angles, 1) acute angle, 2) obtuse angle, and 3) right or right-angled triangles.

The differences between the types are given below:

Types of Triangles

Apart from the above three types, there is Equiangular Triangle with all three internal angles equal to 60°and thus have all sides equal similar to an Equilateral Triangle

Last modified on April 22nd, 2021

One response to “Triangle”

  1. Hi,
    your site is very good and also very much helpful.but i have some problem which i can not solve.i have read every triangle theory from your site but i like to inform you that if you add some more theory like the relationship between 2 right triangle or 2 isoscale or other triangles,it will be more effective for us.so,i am requesting you to add them for us.if you reply me,i will be very greatful to you.
    Thank you.
    Rubaet Alam Rumon

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