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RD Sharma Solutions for Class 9 Maths Chapter 12 - Heron's Formula

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Last updated date: 23rd Apr 2024
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RD Sharma Class 9 Maths Heron's Formula Solutions - Free PDF Download

Free PDF download of RD Sharma Solutions for Class 9 Maths Chapter 12 - Heron's Formula solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 12 - Heron's Formula Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register for online coaching for JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams. 

Register Online for Class 9 Science tuition on Vedantu to score more marks in your examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for the better solutions ,can download Class 9 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

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Class 9 Maths Chapter 12 RD Sharma Solutions for - Heron's Formula

What is Heron's Formula?

The Heron Formula is used to determine the area of ​​a triangle where the length of all their sides is given or the location of the quadrilaterals. We also know it as a Hero formula. This location finding formula does not depend on the angles of the triangle. It depends only on the length of all the sides of the triangle. It contains the word "s" known as the semi-perimeter, which is obtained by dividing the triangle into a triangle. Similarly, the concept of location acquisition is expanded to determine the location of quadrilaterals.

Heron of Alexandria was the first to give Heron's Formula. It is used to locate different types of triangles such as equal triangles, isosceles, be scalene triangles, or quadrilaterals. In this article, we will find out how to determine the area of ​​a triangle or quadrilateral using the Heron formula using examples. Stay tuned to learn more about it.

History of Heron Formula

Heron's formula was written by Heron of Alexandria in 60 CE . Heron was a Greek Engineer and mathematician who calculated the area of ​​a triangle using only the sides of its sides and extended it to calculate quadrilateral areas. He used this formula to prove trigonometric rules such as cosine Laws or cotangent Laws.

Heron’s Formula Definition

According to the Heron Formula, the area value of any triangle with a length, a, b, c, the circumference of a triangle, P, and a fraction of a triangle as s is determined using the formula given below:

Area of the triangle ABC = √s (s-a) (s-b) (s-c), where s = Perimeter / 2 = (a + b + c) / 2

Example: Find the area of ​​a triangle which is 5 units long, 6 units, and 9 units respectively.

Solution: we know that, a = 5 units, b = 6 units and c = 9 units

Thus, Semi-perimeter, s = (a + b + c) / 2 = (5 + 6 + 9) / 2 = 10 units

Location of triangle = √ (s (s-a) (s-b) (s-c)) = √ (10 (10-5) (10-6) (10-9))

⇒ The position of the triangle = √ (10 × 5 × 4 × 1) = √200 = 14.142 unit2

∴ The area of ​​the triangle is 14.142 unit2

How Do You Get a Location Using Heron Formula?

The steps to determine a Location using the Heron Formula are:

  • Step 1: To Find the perimeter of the given triangle.

  • Step 2: Find the semi-perimeter by dividing the perimeter.

  • Step 3: Find the location of the triangle using the Heron Formula which is  √ (s (s) - a) (s - b) (s - c)).

  • Step 4: Once the value is fixed, write the unit at the end (for example, m2, cm2, or in 2).

Heron Formula Applications

Heron Formula has many applications of course:

  • It can be used to determine the location of different types of triangles if the lengths of their different sides are given.

  • It can be used to determine the quadrilateral position if the length of all its sides is given.

Topics Related to Heron Formula

  • Heron's Formula Calculator

  • Triangle location

  • Location of Triangle Calculator

  • Scalene Triangle location

  • Quadrilateral location

  • Quadrilateral calculator location

FAQs on RD Sharma Solutions for Class 9 Maths Chapter 12 - Heron's Formula

1. What is the main purpose of RD Sharma Solutions for Class 9 Maths Chapter 12?

Students who want to strengthen their problem-solving skills and get good grades are encouraged to pursue the RD Sharma Solutions created by professional experts. These solutions in clear format aim to help students grasp ideas in detail and clear their doubts quickly. Students can re-evaluate their answers while reviewing textbook problems and know their level of preparation. The available RD Sharma solutions have been carefully written with great care and attention for students for class 9. Solutions are based on new and different concepts which are introduced in the mathematical syllabus.

2. Name the key benefits of RD Sharma Solutions for Class 9 Maths Chapter 12

The following are the key benefits of RD Sharma Solutions for Class 9 Maths Chapter 12

Students can easily download solutions for each activity to better understand the concepts.

  • Graphs and pictures are provided to help learners grasp ideas easily.

  • Solutions are made by Vedantu experienced teachers in a comprehensive way.

  • Well-organized content

  • The corresponding formulas are highlighted

  • Easy to understand language and free definitions of jargon

  • Designed for trained teachers

  • The latest questions with solutions from the updated smart syllabus

  • Complete analysis of last year's questionnaires

A team of experts have developed clear solutions to improve problem-solving skills among students. For a clearer view of Heron's Formula, students can refer to the materials available at Vedantu.

3. How many exercises are in the formula for Heron's Class 9?

There are only two tests in chapter 12 of Heron's formula. In the first task, you need to find the location of the triangle using the Heron Formula. In the second task, you must find the location of the quadrilaterals. To find the quadrilateral space we divide it into different triangles. NCERT solutions are very important in developing problem skills and understanding all the key points of the chapter. Here we have the details of all the steps step by step so you know the concepts easily.

4. How important is RD Sharma Solutions Class 9 Chapter 12 Heron’s Formula?

RD Sharma Solutions for Class Mathematics Solutions 9 Chapter 12 - The Heron Formula is provided here. The Heron formula is a basic concept that is gaining traction in many areas and is included in the first CBSE Syllabus Program for Class 9 Maths. Therefore, it is important that you clearly understand this concept. And one of the best ways to do that is to refer to NCERT Solutions for Class 9 Maths Chapter 12 of Heron's Formula. These solutions are designed by experienced teachers with years of experience in line with the latest syllabus update of the CBSE 2024-25 term.RD Sharma Class 9 Solutions aims to equip students with detailed and intelligent explanations of all the answers to the questions provided in practice in this Chapter. Therefore, one of the best guides you can familiarize yourself with your learning needs is RD Sharma Solutions. Appropriate topics are presented in an easy-to-understand way, preventing the use of any complex jargon. In addition, its content is updated according to the final smart syllabus of the CBSE term and its guidelines.

5. What is Heron’s formula used for in Class 9 Chapter 12?

In geometry, Heron's formula (sometimes called Heron's formula), named after the Heron of Alexandria, provides the location of a triangle where the lengths of all three sides are known. The formula is called Heron (or Hero) of Alexandria, and evidence can be found in his book Metrica, dated to about AD 60. It has been suggested that Archimedes knew this formula two centuries earlier, 3 and as Metrica collects mathematical knowledge. Found in the ancient world, it is possible that the formula preceded the reference given to that work.