Heron’s Formula Class 9 Free Notes Maths Chapter 12 | Class 9 Heron’s Formula Notes | Edugrown

CBSE Class 9 Maths Notes Chapter 12 Heron’s Formula Pdf free download is part of Class 9 Maths Notes for Quick Revision. Here we have given NCERT Class 9 Maths Notes Chapter 12 Heron’s Formula. According to new CBSE Exam Pattern, MCQ Questions for Class 9 Maths Carries 20 Marks.

NCERT Class 9 Notes becomes a vital resource for all the students to self-study from NCERT textbooks carefully. That is why we have arranged every important points given in the chapter and simplified them so you can easily understand every point clearly. Through these notes a student can boost their preparation and assessment of understood concepts. It is quite easy to retain the answers once you are fully aware of the concept thus notes can be beneficial for you. As you already know the importance of NCERT textbooks for Class 9 thus these NCERT Notes is prove very useful during the preparation of exams. 

Quick Revision Notes of Ch-12 Heron’s Formula Class 9th Maths.

First, we learn about Basis Parameters of Triangles

1. Triangle: A plane figure bounded by three line segments is called a triangle.
In ΔABC has
(i) three vertices, namely A, B and C.
(ii) three sides, namely AB, BC and CA.
(iii) three angles, namely ∠A, ∠B and ∠C.

2. Types of Triangle on the Basis of Sides
(i) Equilateral triangle: A triangle having all sides equal is called an equilateral triangle.
In equilateral ΔABC,
i.e., AB = BC = CA
(ii) Isosceles triangle: A triangle having two sides equal is called an isosceles triangle.
In isosceles ΔABC,
i.e., AB = AC
(iii) Scalene triangle: A triangle in which all the sides are of different lengths is called a scalene triangle.
In scalene ΔABC,
i.e., AB ≠ BC ≠ CA

Perimeter of Triangle

It is the outside boundary of any closed shape. To find the perimeter we need to add all the sides of the given shape.

The perimeter of a rectangle is the sum of its all sides. Its unit is same as of its length.

Perimeter = 3 + 7 + 3 + 7 cm

Perimeter of rectangle = 20 cm

Area

Area of any closed figure is the surface enclosed by the perimeter. Its unit is square of the unit of the length.

Area of a triangle

The general formula to find the area of a triangle, if the height is given, is

Area of a Right Angled Triangle

If we have to find the area of a right-angled triangle then we can use the above formula directly by taking the two sides having the right angle one as the base and one as height.

Here base = 3 cm and height = 4 cm

Area of triangle = 1/2 × 3 × 4 = 6 cm ²

Remark: If you take base as 4 cm and height as 3 cm then also the area of the triangle will remain the same.

Area of Equilateral Triangle

If all the three sides are equal then it is said to be an equilateral triangle.

In the equilateral triangle, first, we need to find the height by making the median of the triangle.

Here the equilateral triangle has three equal sides i.e. 10 cm.

If we take the midpoint of BC then it will divide the triangle into two right angle triangle.

Now we can use the Pythagoras theorem to find the height of the triangle.

AB² = AD² + BD²

(10)² = AD² + (5)²

AD² = (10)² – (5)²

AD² = 100 – 25 = 75

AD = 5√3

Now we can find the area of triangle by

Area of triangle = 1/2 × base × height

= 1/2 × 10 × 5√3 =  25√3 cm²

Area of Isosceles Triangle

In the isosceles triangle also we need to find the height of the triangle then calculate the area of the triangle.

Here,

Area of a Triangle – by Heron’s Formula

When it is not possible to find the height of the triangle easily and measures of all the three sides are known then we use Heron’s formula, which is given by:
Area of a triangle = 

where a, b and c are the sides of the triangle and s = semi-perimeter, i.e. half the perimeter of the triangle = (a+b+c)/2

Area of an Equilateral Triangle

Let the side of the equilateral triangle be ‘a’.

⇒ Area of the triangle

Thus, area of an equilateral triangle = √3/4 × side²