What is a TRIANGLE and How To Calculate the Area of a Triangle?

Triangle is a two-dimensional plane figure or a triangle is a polygon with three angles, three sides, and three vertices. In other words, the triangle is a close figure with three straight lines. We see a number of objects which are made in the shape of a triangle in our daily life.

Types of Triangle

There are many types of triangles like it is defined as:

  1. Equilateral triangle: Equilateral triangle refers to that triangle which has equal sides and each angle is of 60`. All three sides are equal in this.
  2. Right angled triangle: Right angle triangle refers to that triangle in which one angle makes the angle of 90`. And in this, sum of hypotenuse is equal to the sum of perpendicular side plus sum of base side.
  3. Scalene triangle: Scalene triangle refers to that triangle which has three sides and all sides has different length.
  4. Isosceles triangle: Isosceles triangle refers to that triangle in which two sides of a triangle are equal and one side is different.
  5. Acute triangle: Acute triangle refer to that triangle in which all the interior angle is of less then 90`
  6. Obtuse angle triangle: Obtuse angle triangle refers to that in which all the interior angle is more then 90`.

Area of a Triangle

The area of the triangle means the total area that is occupied by the three sides of a triangle. We calculate the area of a triangle always in square units like cm2

The basic formula to calculate the area of a triangle is:

A=1/2BH

Area of a Triangle
Area of a Triangle

Here ‘B’ denotes breadth and ‘H’ denotes height. This formula is put in a question to calculate the area of the triangle when both height and breadth are given in the question. This formula is put basically in all triangles whether it is an equilateral triangle, isosceles triangle, etc.

Let us clear this formula with the help of some examples:

Example 1: Calculate the area of a triangle with a base is 16cm and height is 8cm.

Solution: Now, by putting the formula of area of a triangle:

A=1/2* b*h

Then putting the value of base and height in the formula: A=1/2*16*8

A=18*8
A=64cm2

Example 2. Calculate the area of a triangle with a base is 4 cm and height is 6 cm.

Solution: Now, by putting the formula of area of the triangle.

A=1/2*b*h
A=1/2*4*6
A=2*6
A= 12cm2

Area of a Triangle Formula

There are different formulas to calculate the area of different triangles.

1. Area of an equilateral triangle:

A= √3/4 a2

Thus formula can also be written as:
A=√3/4 (side)2
Here, a denotes the side of a triangle.

Let us clear this formula with an example:

Example 1

Let the side of a given triangle be 4cm.
Then, we can calculate the area of a triangle by putting the formula:

A=√3/4 (side)2
A= √3/4*4*4
A= 6.92cm2

Example 2

Let us take another example to calculate the area of an equilateral triangle:

Let the side of a given triangle be 16cm.

Then the area of triangle will be: A=√3/4 (side)2 A=√3/41616 A=√3416 A= 110.8 cm2

Heron’s formula:

We can also calculate the area of triangle by putting the Heron’s formula. This formula is used only when the side of all three sides of a triangle is given in the question.

Heron’s formula is: A=√s(s-a)(s-b)(s-c)

Here, s denotes for the semi perimeter of a triangle. So we have to follow the given steps to find the area from the Heron’s formula.

Step1: Firstly, we calculate the perimeter of the triangle.

Perimeter: Perimeter means the distance covered by the threw sides of a triangle. It is calculated by adding all three sides of the triangle. P= (a+ b+ c) Here, a, b and c denote the three different sides of a triangle.

Step 2: After calculating the perimeter, we have to calculate the semi perimeter of the triangle.

Semi perimeter: Semi perimeter means the half of the perimeter and it is calculated by the given formula: S= (a+ b+ c)/2 For example, If we ask to calculate the semi perimeter of a triangle with sides, 2cm each.

Then, we can calculate the semi perimeter of a triangle by: S= (2+2+2)/2 S=6/2 S=3.

Step3: Put the value of the semi perimeter and the value of other three sides of a triangle to calculate the area.

Example 1

Let that the three sides of an given triangle is 8cm, 3cm and 9cm. Then calculate the area of a triangle by using heron’s formula.

Sol: Firstly, we calculate the perimeter of a given triangle. P=8+3+9 P= 20 Then we calculate the semi perimeter of the triangle. S=p/2 S=20/2 S= 10 Then we put the value of semi perimeter in the heron’s formula to calculate the area of triangle. A=√s(s-a)(s-b)(s-c) A=√10(10-8)(10-3)(10-9) A=√10271
A=√140
A=11.8cm2

Example 2

Find the area of triangle by using the heron’s formula with sides 3m, 4m, and 5m.
Sol:
Firstly, we calculate the perimeter of the given triangle by adding all three sides.

P= a+b+c
Then, the perimeter will be:
P= 3+4+5
P= 12m


Now, we calculate the semi perimeter of an given triangle.

S=( a+b+c)/2
Then,
S= (3+4+5)/2
S= 12/2
S=6

Now, put the heron’s formula:

A= √s(s-a)(s-b)(s-c)
A= √6(6-3)(6-4)(6-5)
A= √632*1
A= √36
A=6m2

Also, Check How to Calculate the Area of a Circle