by Tiwari Academy
NCERT Complete Solutions for Class 9 Maths Chapter 10 Heron’s Formula in English and Hindi Medium for session 2025-26. Class 9 students often seek effective study materials for mastering topics like Heron’s Formula in their NCERT Maths Textbook Chapter 10. This chapter introduces the concept of calculating the area of a triangle using a formula that simplifies real-life applications of geometry. Resources such as Class 9 NCERT Mathematics Chapter 10 solutions provide step-by-step guidance, helping students solve both NCERT textbook solutions and practice problems efficiently. For better understanding, many students prefer using Heron’s Formula Class 9 NCERT Math solutions, which explain the formula in detail and offer examples for better conceptual clarity.
Class 9 Maths Chapter 10 Solutions: CBSE Board
To ensure maximum preparation, students can download NCERT Exercise Class 9 Mathematics Chapter 10 solutions PDF or refer to solved exercises like Class 9 Maths Book Chapter 10 exercise 10.1 solutions, which include questions directly from the textbook. Using such structured solutions, students can confidently tackle Heron’s Formula application in exams. Online platforms Tiwari Academy offers features for students to ask questions and seek clarification on specific math problems or concepts using Discussion forum. All the questions of class 9th Maths chapter 10 are updated according to revised syllabus and new NCERT book for CBSE 2025-26.
Class 9 Maths Exercise 10.1 in English
NCERT Class 9 Maths Chapter 10 notes are a valuable resource for understanding Heron’s Formula and its practical applications. NCERT 9th Mathematics notes typically condense the theory while emphasizing solved examples and Heron’s Formula practice problems. Students who use such materials gain a deeper insight into how to approach NCERT Class 9 Mathematics Chapter 10 problem-solving. The notes also include NCERT Textbook solutions for Heron’s Formula along with worked-out Heron’s Formula solved examples.
Class 9 Maths Chapter 10 Solutions: State Boards
To further prepare for exams, students can download a Class 9 Math NCERT Book Chapter 10 solution guide, which includes exercises from the textbook and additional problems for practice. Whether accessing NCERT Maths Class 9 Chapter 10 Exercise solutions in PDF format or solving worksheets, students can strengthen their grasp of this critical topic. These resources ensure comprehensive preparation, enabling students to apply the Heron’s Formula area of triangle effectively.
Class 9 Maths Chapter 10 Exercise 10.1
Class 9 Maths Chapter 10 Exercise 10.2
Class 9 Maths Chapter 10 Exercise 10.3
Class 9 Maths Chapter 10 Exercise 10.4
Class 9 Maths Chapter 10 Exercise 10.5
Class 9 Maths Chapter 10 Exercise 10.6
When revising Heron’s Formula NCERT Mathematics Class 9 exercise solutions, students often focus on NCERT Textbook Class 9th Maths Chapter 10 questions and answers to enhance their problem-solving skills. These include both theoretical explanations and practical exercises, ensuring thorough preparation. NCERT Class 9 Math Chapter 10 Exercise solution PDF download allows students to access detailed explanations offline, offering convenience and flexibility. Educators recommend solving Heron’s Formula NCERT Mathematics exercise solutions and working on Class 9 Maths Heron’s Formula worksheets. This combination ensures that students can confidently solve any problem related to Heron’s Formula step-by-step solutions.
Class 9 Maths Chapter 10 Solutions: Hindi Medium
Practicing Heron’s Formula application in Class 9 Math not only boosts their confidence but also prepares them for competitive exams. By using tools like Heron’s Formula NCERT Mathematics textbook solutions, students can excel in exams and build a strong foundation in geometry. This can be particularly helpful for clearing doubts and gaining a deeper understanding. We provide supplementary resources such as video lessons, quizzes and study tips, which can enhance the overall learning experience and cater to different learning preferences.
| Class: 9 | Mathematics |
| Chapter 10: | Heron’s Formula |
| Number of Exercises: | 1 (One) |
| Content Type: | Images, Text, PDF and Videos |
| Educational Session: | CBSE 2025-26 |
| Medium: | Hindi and English Medium |
Important Points in Class 9 Maths Chapter 10 for Annual Exams
Understand Heron’s Formula to calculate the area of a triangle using semi-perimeters.
Practice NCERT solutions for Heron’s Formula and solved examples.
Focus on Class 9 Maths Chapter 10 questions and answers.
Revise key formulas and steps in Heron’s Formula exercise solutions.
Solve practice worksheets regularly.
| Day | Task | Resources |
|---|---|---|
| Day 1 | Understand the theory of Heron’s Formula | Class 9 Maths Chapter 10 Notes |
| Day 2 | Solve examples from the NCERT textbook | Heron’s Formula Solved Examples |
| Day 3 | Practice exercise 10.1 questions | Class 9 Maths Chapter 10 Exercise Solutions |
| Day 4 | Revise important formulas and steps | Heron’s Formula Practice Problems |
| Day 5 | Attempt mock tests and additional problems | Class 9 Maths Chapter 10 Worksheets |
Class 9 Maths Study Material for 2025-26
NCERT Solutions for Class 9 Maths Chapter 10
All the solutions for class 9 Mathematics are updated for new academic session 2025-26 to download in PDF format free of cost. Download Prashnavali 10.1 in Hindi Medium also new academic session 2025-26. UP Board students are now officially using NCERT Textbooks. So, download UP Board Solutions for Class 9 Maths Chapter 10 all exercise here in English and Hindi Medium. All NCERT Solutions for standard 9 (High School) for 2025-26 are available Online as well as Offline mode of contents. Class 9 Maths Chapter 10 Solutions in Videos are also available. Online and Offline Apps of Tiwari Academy for 2025-26 in Hindi Medium and English Medium are also available on Play Store as well as App Store.
Class 9 Maths Chapter 10 Practice Questions with Solution
What is Heron’s Formula?
Heron’s Formula: The formula given by Heron about the area of a triangle is known as Heron’s formula.
According to this formula, area of triangle = √[s (s – a)(s – b)(s – c)], where a, b and c are three sides of the triangle and s is the semi-perimeter.
This formula is also used for finding the area of quadrilateral. In quadrilateral, we join one diagonal to divide the quadrilateral into two triangles and then find the area of each triangle separately by Heron’s formula.
What is the formula for Area of an equilateral triangle?
Area of equilateral triangle: Let the side of an equilateral triangle be k. Then, area of an equilateral triangle = (√3/4) k². Square units and altitude = (√3/2) k units.
9th Maths Chapter 10 Solutions in English & Hindi Medium
Get here the updated NCERT Solutions for Class 9 Math Chapter 10 Heron’s Formula Exercise 10.1 in Hindi and English Language format. Question Answers are given given below and these are updated for new academic year 2025-26. UP Board Students can also use these solutions for there board exams. Class 9 Maths NCERT Solutions are applicable for CBSE, UP Board, MP Board, Gujrat Board, etc., whoever is following CBSE Syllabus 2025-26.
Important Questions on 9th Maths Chapter 10
There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
Here, the sides of triangle are a = 15 m, b = 11 m and c = 6 m.
So, the semi-perimeter of triangle is given by s = (a + b + c)/2 = (15 + 11 + 6)/2 = 32/2 =16 m
Therefore, using Heron’s formula, the area of triangle
= √(s(s – a)(s – b)(s – c) )
= √(16(16 – 15)(16 – 11)(16 – 6) )
= √(16(1)(5)(10) )
= √(4 × 4 ×(1)(5)(5 × 2) )
= 4 × 5 √2 = 20 √2 m²
Hence, the area painted in colour is 20√2 m².
Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm.
Here, the sides of triangle are a = 18 cm, b = 10 cm and perimeter is 42 cm.
We know that the perimeter of triangle = a + b + c
⇒ 42 = 18 + 10 + c ⇒ c = 14 cm
So, the semi-perimeter of triangle is given by
s = (a + b + c)/2 = 42/2 = 21 cm
Therefore, using Heron’s formula, the area of triangle
= √(s(s – a)(s – b)(s – c) )
= √(21(21 – 18)(21 – 10)(21 – 14) )
= √(21(3)(11)(7) )
= √(7 × 3 × (3)(11)(7) )
= 7 × 3√11 = 21√11 cm²
Hence, the area of triangle is 21√11 cm².
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Perimeter of triangle = 540 cm
The ratio of sides of triangle = 12:17:25
Let, one of the sides of triangle a = 12x
Therefore, remaining two sides are b = 17x and c = 25x.
We know that the perimeter of triangle = a + b + c
⇒ 540 = 12x + 17x + 25x
⇒ 540 = 54x
⇒ x = 540/54 = 10
So, the sides of triangle are
a = 12 × 10 =120 cm,
b = 17 × 10 = 170 cm and
c = 25 × 10 =250 cm.
So, the semi-perimeter of triangle is given by
s = (a + b + c)/2 = 540/2 = 270 cm
Therefore, using Heron’s formula, the area of triangle
= √(s(s – a)(s – b)(s – c) )
= √(270(270 – 120)(270 – 170)(270 – 250) )
= √(270(150)(100)(20) )
= √81000000
= 9000 cm²
Hence, the area of triangle is 9000 cm².
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Perimeter of triangle = 30 cm
Two sides of triangle b = 12 cm and c = 12 cm.
Let, the third side = a cm
We know that the perimeter of triangle
= a + b + c ⇒ 30 = a + 12 + 12
⇒ 30 – 24 = a ⇒ a = 6
So, the semi-perimeter of triangle is given by
s = (a + b + c)/2 = 30/2 = 15 cm
Therefore, using Heron’s formula, the area of triangle
= √(s(s – a)(s – b)(s – c) )
= √(15(15 – 6)(15 – 12)(15 – 12) )
= √(15(9)(3)(3) )
= 9√15 cm²
Hence, the area of triangle is 9√15 cm².
IMPORTANT FORMULAE AND TERMS ON HERON’S FORMULA
Area of Triangle: The total space inside the boundary of the triangle is known as area of the triangle.
Area of triangle = ½ × base × height
Area of an isosceles triangle: Let B be the base and S be the equal sides of an isosceles triangle, then area of an isosceles triangle = [B√(4S² – B²)]/2 square units.
Perimeter: Perimeter of a triangle is equal to the sum of its three sides. It is denoted by 2s, where s is the semi-perimeter of a triangle.
The importance of NCERT Class 9 Maths Chapter 10 in Exams
NCERT Class 9 Mathematics Textbook Chapter 10, Heron’s Formula, is crucial for exams as it simplifies the calculation of the area of triangles using semi-perimeters. This chapter lays a foundation for advanced geometry concepts. Using Class 9 Maths Chapter 10 solutions helps students gain a step-by-step understanding of the topic. Solving Heron’s Formula NCERT textbook math solutions ensures a grasp of theoretical and practical applications. Practicing Heron’s Formula mathematics exercise solutions and reviewing Class 9 Maths Chapter 10 notes prepare students for solving exam problems accurately. Resources like NCERT Math Heron’s Formula solved examples improve confidence in solving area-related problems.
Importance of Solving Heron’s Formula Practice Problems
Practicing Heron’s Formula practice problems strengthens understanding and improves problem-solving skills. These problems, often included in Class 9 Maths Chapter 10 solution guides and worksheets, help students master applications like the Heron’s Formula area of triangle. By solving Heron’s Formula NCERT exercise solutions and Class 9 Maths Chapter 10 exercise 10.1 solutions, students build confidence for exams. Working on Heron’s Formula solved examples ensures you can handle variations of the problem. Resources such as NCERT Textbook Class 9 Chapter 10 Mathematics solutions provide extensive practice material, equipping students to excel in both school and competitive exams.
How can I effectively prepare for Chapter 10 Heron’s Formula?
To prepare effectively for Heron’s Formula, students should start by studying the theory and working on Class 9 Maths Chapter 10 questions and answers. Referring to Heron’s Formula NCERT textbook exercise solutions helps in understanding problem-solving techniques. Downloading a Class 9 Maths Chapter 10 Exercise solution PDF is a convenient way to practice offline. Solve Heron’s Formula step-by-step solutions and attempt Class 9 Maths Heron’s Formula worksheets for comprehensive practice. Using a Class 9 Maths Chapter 10 solution guide ensures you can solve both textbook problems and real-life geometry applications with ease.
How many problems are there in chapter 10 of class 9th Maths?
In chapter 10 of class 9th Maths, there is only one exercise. This exercise (Ex 10.1) has 6 questions and three examples (examples 1, 2, 3).
Where can I find NCERT solutions for Heron’s Formula?
You can find detailed NCERT detailed solutions for Heron’s Formula in online resources or study guides like the Class 9 Maths Chapter 10 solution PDF download. These solutions include explanations, Heron’s Formula practice problems and NCERT math solved examples. The NCERT Class 9 Maths Chapter 10 solutions PDF can be accessed for offline practice. Many websites and apps like Tiwari Academy provides Heron’s Formula Class 9 NCERT solutions with interactive examples. You can refer to Class 9 Maths Chapter 10 notes, which condense key points and highlight important questions, helping you revise efficiently.
What is Heron’s Formula in chapter 10 of grade 9th Maths?
Heron’s Formula is used to find the area of a triangle. This formula is helpful where it is not possible to find the height of the triangle easily.
How do Heron’s Formula notes and worksheets benefit students?
Class 9 Maths Chapter 10 notes and worksheets are essential for focused revision. Notes highlight key concepts and include examples like Heron’s Formula solved examples for quick reference. Worksheets with Class 9 Maths Heron’s Formula step-by-step solutions offer practice, helping students solve problems efficiently. Accessing resources like Heron’s Formula NCERT textbook solutions or downloading a Class 9 Maths Chapter 10 solution PDF ensures offline accessibility. These materials, combined with Heron’s Formula exercise solutions, simplify complex problems. Consistent use of NCERT Class 9 Maths Chapter 10 questions and answers helps students excel in understanding and application.
Which questions of chapter 10 of grade 9th Maths are compulsory to do for the exams?
Students should do all questions and examples of chapter 10 of class 9th Maths. But examples 2, 3 and questions 2, 3, 5 of exercise 10.1 are compulsory to do for the exams because these are very important questions from an exam point of view. In exams, these questions can come in three marks.
Is chapter 10 Heron’s Formula of grade 9th Maths easy or complicated to solve?
Chapter 10 of class 9th Maths is not easy and not complicated. It lies in the mid of easy and complicated because some examples and questions of this chapter are easy, and some are complicated. However, the difficulty level of any topic varies from student to student. So, Chapter 10 of class 9th Maths is easy or complicated depends on students also. Some students find it challenging, some find it easy, and some find it in the middle of easy and difficult.
How much time is needed to complete chapter 10 of class 9th Maths?
Students need a maximum of 1 week to complete chapter 10 of class 9th Maths if they give a minimum of 1-2 hours per day to this chapter. This time also depends on student’s working speed, efficiency, capability, and many other factors.
