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# Heron's Formula Class 9 Notes CBSE Maths Chapter 10 (Free PDF Download)

Last updated date: 11th Sep 2024
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## Class 9 Maths Revision Notes for Heron's Formula of Chapter 10 - Free PDF Download

To help students to solve the questions based on Heron's formula easily and accurately during exams,  we at Vedantu are providing a free pdf of CBSE Class 9 Maths Chapter 10 Herons Formula notes which will help students to study the chapter effectively as well as score well in the examination. These CBSE Class 9 Maths Herons Formula notes have been prepared by experts who ensure the use of simple language so that students can understand concepts easily and quickly. These notes are a great reference tool and will help students quickly revise all the chapters' important terms before exams. Class 9 students can download Maths Chapter 10 Herons Formula revision notes through the link provided below.

## Topics Covered in Class 9 Maths Chapter 10 - Herons Formula

• Introduction to Herons Formula

• Area of Triangle Using Herons Formula

• Application of Herons Formulas in Finding Area of Quadrilateral

Also, check CBSE Class 9 Maths revision notes for all chapters:

Competitive Exams after 12th Science

## Access Class-9 Mathematics Chapter 10 – Heron’s Formula Notes in 30 Minutes

Area of Triangle:

• Area of a triangle when height is known is given by $Area=\dfrac{1}{2}\times base\times height$

• For example: Let a triangle ABC

In the triangle ABC height is $4cm$ and base is $3cm$

Therefore, area of triangle ABC is given by

$Area=\dfrac{1}{2}\times base\times height$

$Area=\dfrac{1}{2}\times 3\times 4$

$Area=6c{{m}^{2}}$

• This formula can be used to find the area of right-angle triangle, equilateral triangle and isosceles triangle.

• But when it is difficult to find the height of the triangle like in the case of scalene triangle, we use heron’s formula for calculating the area of triangle

Area of Triangle – by Heron’s Formula:

• Heron’s formula for calculating the area of triangle was given by mathematician Heron around $60$ CE

• Area of triangle by heron’s formula is given by$Area=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$

Where, $a,b,c$ are the sides of triangle and $s$ is semi-perimeter of triangle

• Semi perimeter of triangle is the half of perimeter of triangle and is given by $s=\dfrac{a+b+c}{2}$

• Heron’s Formula is very helpful where it is not possible to find the height of a triangle.

• For example: Let a triangle ABC

Sides of triangles are

$a=24cm$

$b=40cm$

$c=32cm$

Perimeter of triangle is given by

$Perimeter=a+b+c$

$Perimeter=24+40+32$

$Perimeter=96cm$

Semi perimeter is given by

$s=\dfrac{perimeter}{2}$

$s=\dfrac{96}{2}$

$s=48cm$

Now, area of triangle is given by

$Area=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$

$Area=\sqrt{48\left( 48-24 \right)\left( 48-40 \right)\left( 48-32 \right)}$

$Area=\sqrt{48\left( 24 \right)\left( 8 \right)\left( 16 \right)}$

$Area=\sqrt{147456}$

$Area=384c{{m}^{2}}$

Area of Quadrilateral using Heron’s Formula:

• A quadrilateral can be divided into two triangular parts by joining one of its diagonals

• And then with help of Heron’s Formula we can find the area of two triangular parts

• Then by adding them we can get the area of the quadrilateral.

• For example: Let a rhombus ABCD

Area of triangle ABD is given by

$Are{{a}_{1}}=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$

Here, $a=100cm,b=100cm,c=160cm$

And semi perimeter is

$s=\dfrac{a+b+c}{2}$

$s=\dfrac{100+100+160}{2}$

$s=\dfrac{360}{2}$

$s=180cm$

$\therefore Are{{a}_{1}}=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$

$Are{{a}_{1}}=\sqrt{180\left( 180-100 \right)\left( 180-100 \right)\left( 180-160 \right)}$

$Are{{a}_{1}}=\sqrt{180\left( 80 \right)\left( 80 \right)\left( 20 \right)}$

$Are{{a}_{1}}=\sqrt{23040000}$

$Are{{a}_{1}}=4800c{{m}^{2}}$

Now, area of triangle BCD is given by

$Are{{a}_{2}}=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$

Here, $a=100cm,b=100cm,c=160cm$

And semi perimeter is

$s=\dfrac{a+b+c}{2}$

$s=\dfrac{100+100+160}{2}$

$s=\dfrac{360}{2}$

$s=180cm$

$\therefore Are{{a}_{2}}=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$

$Are{{a}_{2}}=\sqrt{180\left( 180-100 \right)\left( 180-100 \right)\left( 180-160 \right)}$

$Are{{a}_{2}}=\sqrt{180\left( 80 \right)\left( 80 \right)\left( 20 \right)}$

$Are{{a}_{2}}=\sqrt{23040000}$

$Are{{a}_{2}}=4800c{{m}^{2}}$

$\therefore AreaofABCD=Are{{a}_{1}}+Are{{a}_{2}}$

$AreaofABCD=4800+4800$

$AreaofABCD=9600c{{m}^{2}}$

## How to Calculate Area of Triangle Using Herons Formula?

Heron's formula is an important mark in this subject. By this formula, we can calculate the area of the triangle if the length of all three sides is known. This can be calculated using the following two steps:

Step 1: Calculate the “s” (half of the triangle’s perimeter):

S= a+ b = c2

Step 2: Then calculate the Area.

This formula is credited to Hero (or Heron) of Alexandria, a Greek Engineer, and Mathematician in 10 – 70 Anno Domini (AD).

## Benefits of Referring to Vedantu’s Revision Notes of Class 9 Maths Chapter 10

• Refer to these notes if you want to better understand all the topics of Maths Chapter 10 quickly. The easy-to-understand writing format of the notes will strengthen your revision process.

• The Class 9 Maths Chapter 10 revision notes are suitable for students who want to-the-point study resources to brush up on their concepts.

• Being expert-curated, our Class 9 Maths Chapter 10 notes are completely factually correct and contain an accurate description of each chapter concept.

• The free PDF download feature of the Class 9 Maths Chapter 10  revision notes is mostly preferred by the students who want to access the best quality study resources without paying any cost and in the comfort of their homes.

## Important Questions for Practice

1. Find the area of an equilateral triangle with a side of 5 cm.

2. Find the triangle area whose sides are 12 cm, 50 cm, and 60 cm.

3. ABCD is a rhombus whose three vertices, A, B, and C, lie on the circle with a centre of 0. Find the rhombus's area if the radius of a circle is 12 cm.

4. If every side of a triangle is tripled, find the percent increase in the area of the triangle so formed.

If you are a Class 9 student who wants to quickly revise all the important concepts of Heron's formula quickly, then these Class 9 Maths Chapter 10 revision notes are the perfect study material for you. So, download the Herons Formula Class 9 CBSE Maths Chapter 10 Revision Notes today to strengthen your knowledge on this topic.

## Conclusion

Heron's Formula Class 9 Notes CBSE Maths Chapter 10 offers a vital resource for students navigating the intriguing terrain of geometry. These meticulously crafted notes, available as free PDF downloads, demystify the enigmatic Heron's Formula, empowering learners to calculate triangle areas with precision and ease. They provide a comprehensive understanding of this mathematical tool, from its derivation to practical applications. These notes are not just about exam preparation; they equip students with a problem-solving skill set that extends beyond the classroom. With their accessibility and educational value, they serve as indispensable companions for students aiming to excel in their CBSE Class 9 mathematics curriculum.

## FAQs on Heron's Formula Class 9 Notes CBSE Maths Chapter 10 (Free PDF Download)

1. How to find the area of a triangle when the height is given?

The following formula is used to calculate the area of a triangle when its height is known:

Area = ½ × Base × Height

2. What is the semi-perimeter of a triangle?

Semi-perimeter of a triangle is the half of the perimeter of a triangle, and it is given as:

$S=\frac{a+b+c}{2}$

3. Who has introduced Herons formula?

Herons formula to find the area of a triangle is given by Mathematician Heron around 60 CE.

4.  How will the revision notes help the students in their exams?

Students can revise calmly from our notes before the exam. It will not only be a revision but an effective revision. Before the exam going through the chapter becomes tedious and time-consuming, they can resort to these capsuled notes.

5. From where can I get the Class 9 Maths Chapter 10 revision notes?

Class 9 Maths Chapter 10 revision notes can be downloaded free from the pdf provided here. Students are given free access to our revision material owing to the needs of the revision.