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

NCERT Solutions for Class 9 Maths Chapter 12 will teach you the vital conceptions of Heron’s Formula. The formula is itself named after the mathematician Heron who invented this formula a few centuries ago. In previous chapters of NCERT Solutions for Class 9 Maths, you have learned how to calculate the area of different triangles like a right-angle triangle, isosceles triangle, and equilateral triangle. What if you have to measure the area of a scalene triangle, whose sides’ lengths are given? Heron’s Formula helps you to find out the triangle of any scalene triangle, given that it’s all sides are known to you. Not only that, but you can also find the area of all types of triangles through Heron’s Formula.

There are 2 exercises and 15 questions in this chapter. The exercises are given after each topic of the chapter. Maths Class 9 Chapter 12 NCERT Solutions are apt to study the concepts of Heron’s Formula from the very basics. They ensure that you grasp every topic step by step until the chapter ends. The sets of questions in these exercises are ample for anyone to understand and go through the concepts themselves. Besides these exercises, this chapter also contains solved examples which help you in comprehending the concept in a much better way. 

NCERT Solutions Class 9 Chapter 12 covers all the main topics of the chapter such as the area of a triangle by Heron’s Formula and applications of Heron’s Formula. Our experts are proficient when it comes to giving the right solution for the questions mentioned in this NCERT book. Our NCERT solutions will help you in practicing and thus make you confident about your maths exam. 

Topics Covered Under NCERT for Class 9 Maths Chapter 12

CBSE Class 9 Maths Chapter 12 is introduced to state the need to calculate the area of a scalene triangle whose all sides’ lengths are given to you. In previous chapters, you learned the areas of different shapes, which included areas of the square, rectangle, and triangles, triangles such as an equilateral, isosceles, and right-angle triangle. It is vital that you understand the formula and concepts of measuring the area of a scalene triangle too. This formula not only helps you in finding the area of the scalene triangle alone, but you can measure the areas of all other types of triangles. Following we have all the topics that are covered in NCERT Class 9 Maths Chapter 12:

 Heron’s Formula

Heron gave the formula called ‘Heron’s Formula’ to find out the area of a triangle. It is as below:

Area of a triangle = A = √s(s-a)(s-b)(s-c)

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

Heron’s Formula is entirely applicable when it is not possible to find out the height of the triangle easily.

Applications of Heron’s Formula in Finding the Areas of Quadrilaterals

To find out the area of a quadrilateral, there is no such specific formula for it. Heron’s Formula is the only key to find out the area of any quadrilateral whose sides and one diagonal are given. For it, you need to divide the quadrilateral into two different triangles. You can then find out the areas of each of these quadrilaterals and add both of the area measures to get the total. This total sum of two triangle areas will be the area of the given quadrilateral. 

Important Points

  •  An Equilateral Triangle is a triangle whose all sides are equal
  •  An Isosceles Triangle is a triangle whose only two sides measure equal
  •  A right-angled triangle is a triangle whose one angle is a right angle, which means it is angled at 90 degrees.

Exercise wise explanation of NCERT Class 9 Chapter 12 Heron’s Formula

Exercise 12.1

  • In the first exercise of CBSE Class 9 NCERT Maths Chapter 12, you will be asked to solve the questions by using some already-known formulas and the newly read Heron’s Formula, as well. 
  • You may be asked to find out the area of an equilateral triangle using Heron’s Formula. Questions such as finding the area of a triangle who are sides are given, include in this exercise. 
  • You can also be put through a situation where the two sides of the triangles and its perimeter are provided, and you have to find out its area. The sides of the triangle could also be provided in ratios.

Exercise 12.2

  • The questions of the second exercise are based on the sub-topics of your chapter, sequence wise. 
  • This exercise will include the questions which are related to the area of a quadrilateral. Questions will be based on different diagrams where you tend to segregate these diagrams into triangular shapes to solve the whole question. 
  • You will be provided with various sides and angles, with the diagram of shape specifications so that you can assign the measurement to it and solve questions step by step.

Benefits of NCERT Solutions for Class 9 Maths Chapter 12 by Instasolv

  • We provide exercise-wise NCERT solutions for class 9 maths chapter 12. 
  • All our NCERT solutions are based on CBSE syllabus and exam pattern. 
  • We have provided step-wise calculations. 
  • We have the best maths experts for class 9 that is why our NCERT solutions are always 100% error-free. 
  • Our NCERT solutions will help you in solving all your doubts related to Heron’s Formula.