NCERT Solutions for Class 9 Maths Chapter 12 – Heron’s Formula Exercise 12.1

One of the most important and difficult subjects for students in Class 9 is Mathematics. In addition to a solid conceptual understanding, mathematics also necessitates a lot of practice in problem-solving. Practising lots of questions is the key to getting good grades in mathematics during examinations. It is also interesting to note that the majority of exam questions in Class 9 are taken from NCERT textbooks. As a result, the NCERT book is the most crucial tool for practising problem-solving for the annual exams. Keeping this in mind, Extramarks provides NCERT solutions, such as the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1.

The National Council of Educational Research and Training (NCERT) was established by the Union Government to oversee the development of policies to improve school education in India. It was founded in 1961 and offers guidance to the federal as well as state governments on matters related to education policy. The NCERT conducts extensive research to improve schooling in the country. It works in partnership with many academic institutions and international organisations to conduct research to enhance education across the country. It also provides teacher training programmes to help teachers learn cutting-edge teaching strategies. Publication of textbooks and other educational materials is one of the NCERT’s main responsibilities. It also produces newsletters, journals, and other supplementary materials to impart quality education to students of all classes. Moreover, it offers online learning resources for students on its website, including PDF versions of the NCERT textbooks. Reading the NCERT textbooks is the most crucial part of CBSE students’ preparation for their exams, as the NCERT books are recommended by the CBSE. Similarly, the NCERT textbooks also serve as the basis for the syllabuses for a variety of competitive exams, such as Olympiads. Hence, it is essential that students be thorough with the concepts in the NCERT textbook and solve the exercises in it. While solving the exercises, NCERT solutions such as the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 can also be of great help.

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula (Ex 12.1) Exercise 12.1

Even though NCERT solutions are accessible online, it is best to always have access to them without interruption. Students who have access to the NCERT solutions offline can use them whenever and wherever they want. Hence, Extramarks provides the Class 9 Maths Exercise 12.1 Solution in PDF format. Students can download the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 from the Extramarks platform to use whenever they want to learn. Consequently, unforeseen network problems and unreliable internet service would not be a hindrance to learning. All of the questions in Class 9 Maths Chapter 12 Exercise 12.1 of the NCERT textbook are covered by the expert-curated NCERT solutions, offering a chance to learn and get ready for exams. From the Extramarks website and mobile app, students can download the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 in PDF format for consistent exam preparation.

Access NCERT Solutions for Maths Chapter-12 Heron’s Formula

If students have access to the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1, they will be better able to comprehend the concepts presented in the NCERT textbook. They will also be fully informed of the correct answers and strategies for solving each question. Each question in the NCERT textbook can be answered in a structured manner. For students to better understand the chapter’s concepts, the Extramarks website and mobile app both provide access to the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1.

Exercise 12.1

Maths Class 9 Chapter 12 Exercise 12.1 is based on Heron’s Formula. Heron’s Formula is one of the most important concepts to learn for Class 9 students. Students should memorise this formula and learn to apply it while solving problems. This will not only help them in their examinations but also help them in solving numerous problems in their further studies. It is vital that students solve all the questions in this exercise.

Class 9 Maths Exercise 12.1 Solution – All questions

Extramarks provides accurate solutions to all the questions in Exercise 12.1 Class 9 Maths. The NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 are among the most useful resources for students preparing for final exams. Solutions for all of the questions are provided in the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 in a straightforward and understandable format. The NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1 have been written and verified by experts with decades of experience. As a result, they are precise, error-free, and easily dependable. The CBSE guidelines are completely followed in the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 in order to help students achieve the highest marks possible. For the purpose of assisting students in fully understanding the concepts, every detail has been fully explained. To make them simpler to understand, harder problems have been divided into smaller components. Diagrams are used whenever necessary in the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 to help students easily understand the solutions. Therefore, students can use the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 as their go-to resource for trustworthy answers to all the exercise questions.

What is Heron’s Formula: NCERT Solutions for Class 9 Maths Exercise 12.1

Heron’s Formula is a very useful formula in Mensuration. Heron’s Formula helps in finding the area of a triangle when the lengths of its sides are known. This formula was given by the Egyptian Mathematician, Heron and is widely applied in Mathematics. Solving Exercise 12.1 is crucial to understanding Heron’s formula. Students need to learn the right way to use this formula while solving questions. The NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 offered by Extramarks include each and every step necessary to resolve the problems in this exercise, making it simpler for students to find the solution. Students can correctly apply the concepts covered in the chapter by using the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1. The NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 have been carefully put together by teachers with advanced degrees. These solutions are written with Class 9 students’ level of comprehension in mind. To make it simpler to write answers in exams, the problems in this exercise have been broken down into manageable steps. The significance of providing detailed answers in exams is consistently emphasised by examiners. The detailed solutions provided in NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 help in obtaining perfect scores on exams. Many students find it difficult to comprehend and retain the formulas and procedures presented in the NCERT textbook, which prevents them from being able to use them to solve the exercises’ problems. But practising the detailed solutions using the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 makes it simpler to remember and use the formulas correctly. Due to their familiarity with the solutions, students will be at an advantage during their exams. By repeatedly practising NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1, they will be able to answer these questions quickly and accurately in exams.

Class 9 Maths Ex 12.1: Question 1

Question 1 of Exercise 12.1 is based on the application of Heron’s Formula. In this question, students are required to find the area of an equilateral triangle using Heron’s Formula.

Heron’s Formula Exercise 12.1: Question 2

Question 2 of Exercise 12.1 requires students to find the rent that a company will pay on the wall of a flyover that is triangular in shape. Students need to use Heron’s Formula to find the area of the triangular wall and subsequently calculate the rent.

Class 9 Maths Ch 12 Ex 12.1: Question 3

Question 3 of Exercise 12.1 requires students to find the area of one of the walls of a slide in a park whose lengths of the sides are known. Students can use Heron’s formula to find the area as the lengths of the sides are given.

Ex 12.1 Class 9 Maths NCERT Solutions: Question 4

Question 4 of Exercise 12.1 can be tricky for students to solve. Students are given the lengths of two sides of a triangle. The perimeter is also known. Students need to find the area of the given triangle. This can be done by calculating the length of the third side using the perimeter. Students should refer to the NCERT solutions provided by Extramarks to learn the correct method of solving this question.

NCERT Solutions for Class 9

When studying for the Class 9 annual exams, students must use books that comply with CBSE norms. They must use the NCERT textbooks. Students should attempt to answer the questions in the NCERT book, including those found in the examples and exercises, after finishing each chapter. In order to assess their own responses, students must be aware of the correct answers to the questions. As a result, Extramarks offers the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1. The NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 have been provided in a step-by-step format by Extramarks to assist Class 9 students in understanding the problems even when they are trying to solve them for the very first time. Alternative methods for solving some questions that are simpler to understand are also included in Extramarks’ NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1. Students who have access to the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 can test their knowledge and identify their strong and weak areas. Additionally, the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 support students in the acquisition of a variety of skills, including logical and reasoning skills, all while offering critically analysed learning. The NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 also help students prepare effectively for the annual exams, making it a crucial process in exam preparation.

Students require access to a variety of questions as well as solutions that are fully explained before they appear for their exams. A large percentage of question banks base their content primarily on the exercises from NCERT textbooks. When students have access to the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1, answering questions is made simpler. It helps them understand the ideas more quickly. Students feel more prepared for any exam if they can understand concepts quickly. This allows them to maintain their attention and concentration while having more time to focus on other subjects. By comprehending the topics covered in the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1, students can make constant academic progress. The chapter’s content can occasionally be difficult and perplexing, but having access to the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 that are adapted to students’ needs can be a helpful study resource. Using these learning resources will make it easier to learn Heron’s Formula. For students who want to advance consistently while completing other papers, the NCERT problems are a useful exercise. The NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 by Extramarks focuses on a particular topic of the chapter. For students who wish to perform better on their exams, there are many study resources available at Extramarks, including chapter-wise worksheets and mock tests. Extramarks acts as a one-stop destination for practising, studying, and testing. Since Extramarks’ NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 are written and edited by subject specialists, all students are ensured of a smooth educational experience.

CBSE Study Materials for Class 9

The Central Board of Secondary Education (CBSE) is one of India’s major school governing bodies. It has the greatest number of students enrolled. Additionally, thousands of schools are affiliated with it. The CBSE is in charge of the CBSE board examination that is taken in Class 10. However, the concepts in Class 9 are equally important to understand as the ones taught in Class 10. Class 9 involves multiple exams at the school level. Students become anxious as they study for multiple exams. They are unable to adequately prepare for the exams, preventing them from putting forth their best effort. Consequently, they are unable to achieve the desired results. Nonetheless, by employing effective preparation techniques and utilising the best study materials available, students can overcome their fear of exams. One of the best methods for exam preparation is to practice the NCERT solutions, like the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1. In the exams, a number of questions are drawn from the NCERT exercises. With this in mind, Extramarks provides the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1. By having access to the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1, students can improve their understanding of the chapter and better prepare for the chapter’s questions.

CBSE Study Materials

The mission of Extramarks is to facilitate learning for students. Extramarks provides a variety of study materials to help CBSE students in every possible way. Students are assisted in understanding the subjects they are studying by the 3D animations and graphics, which also make the subjects interesting to study. Some of the best instructors in the nation work at Extramarks, and they greatly simplify learning for students. In addition to the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1, Extramarks offers a number of practice tests, multiple-choice questions, and interactive activities. Students who use Extramarks for their study needs can prepare fully for their exams and score better marks. Before the exams, students’ confidence and morale are boosted thanks to the guidance offered by Extramarks. They can take on the exams fearlessly and perform to their highest potential.

Q.1 A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

Ans

Side of equlateral triangle=aArea of triangle                Δ=s(s−a)(s−b)(s−c)     [Heron’s Formula]where, s=a+b+c2            =a+a+a2            =3a2∴           Δ=3a2(3a2−a)(3a2−a)(3a2−a)            =3a2×a2×a2×a2            =a2×a23            =34a2 square units.If perimeter of triangle(3a)            =180 cm            a=1803=60 cmThen, area of equilateral triangular signal board           =34(60)2 square cm           =9003 cm2Thus, the area of the traffic signal board is 9003 cm2.

Q.2 The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see following figure.). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?

Ans

The sides of triangular walls are 122 m, 22 m and 120 m.Area of triangle             Δ=s(s−a)(s−b)(s−c)      [Heron’s Formula]where, s=a+b+c2 and a=122 m,b=22 m and c=120 m.             s=122+22+1202               =2642               =132 m            Δ=132(132−122)(132−22)(132−120)               =132×10×110×12              =1320 m2Thus, the area of one wall is 1320 m2.Earning of 1m2 wall by the advertisement in 1 year               =₹5000Earning of 1m2 wall by the advertisement in 3 months               =₹500012×3               =₹1250Earning of 1320 m2 wall by the advertisement in 3 months               =₹1250×1320              =₹1650000Thus, the company paid the rent for one wall is ₹1650000.

Q.3 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 15m, 11 m and 6 m, find the area painted in colour.

Ans

The sides of the wall are 15m, 11 m and 6 m.Heron’s Formula:          Δ=s(s−a)(s−b)(s−c)where, s=a+b+c2 and a=15 m,b=11 m and c=6 m.          s=15+11+62            =322            =16 m          Δ=16(16−15)(16−11)(16−6)            =16×1×5×10            =202 m2Thus, the painted area of wall is 202 m2.

Q.4 Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.

Ans

Two sides of triangle are 18 cm and 10 cm.Perimeter of triangle=42 cm                a+b+c=42              18+10+c=42                        c=42−28                          =14Area of triangle by Heron’s formula,                      Δ=s(s−a)(s−b)(s−c)                       s=a+b+c2                         =422=21                      Δ=21(21−18)(21−10)(21−14)                         =21×3×11×7                         =2111 cm2Thus, the area of triangle is 2111 cm2.

Q.5 Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find its area.

Ans

Ratio of sides of triangle=12:17:25        Perimeter of triangle=540 cmLet a=12 k, b=17 k and 25 kthen,   12k+17k+25k=540                           54 k=540⇒                          k=10So,​ a=12×10=120 cm         b=14×10=170 cm         c=25×10=250 cmArea of triangle, by Heron’s Formula:       Δ=s(s−a)(s−b)(s−c)       s=a+b+c2=5402=270      Δ=s(s−a)(s−b)(s−c)      =270(270−120)(270−170)(270−250)       =270(150)(100)(20)       =270(150)(100)(20)       =9000 cm2Thus, the area of triangle is 9000 cm2.

Q.6 An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Ans

Perimeter of isosceles triangle=30 cm                   Each of the equal side=12 cm         Then, third side of triangle=30−12−12                                       =6 cmArea of triangle, Δ=s(s−a)(s−b)(s−c)  [Heron’s Formula]                         s=a+b+c2                       =302=15                     Δ=15(15−12)(15−12)(15−6)                           =15(3)(3)(9)                           =915 cm2Thus, the area of isosceles triangle is 915 cm2.

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FAQs (Frequently Asked Questions)

1. Where can students find the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1?

The NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 can be found in PDF format on the Extramarks website and mobile application. For eventual practice, they can also download the PDF document. Even if they are not online, they can still attempt the NCERT questions and check their solutions. In addition, they can find a variety of other study materials for thorough and comprehensive exam preparation.

2. Do Class 9 examinations include questions from the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1?

From an examination perspective, the NCERT Solutions For Class 9 Maths Chapter 12 Exercise 12.1 offered by Extramarks are very significant. In the exams, a lot of these questions are found repeatedly. They are based on some important concepts of the chapter and are likely to come up in exams.