NCERT Solutions for Class 9 Maths Exercise 12.2 Heron’s Formula in Hindi and English medium updated for new academic session 2022-2023. Exercise 12.2 of Class 9 Maths contains 9 questions in all. Most of the questions are easy to understand and solve. A few students find question number 9 as difficult to solve.
NCERT Solutions for Class 9 Maths Exercise 12.2
Contribution of Mathematicians
Till now you have studied a lot of Greek mathematicians and their important contributions but for us, in India, there is Bhaskara II. He was an Indian mathematician and astronomer who contributed to arithmetic, algebra, and mathematics of planets.
He also discovered the principles of calculus. In the second part of chapter 12 from NCERT solutions for Maths class 9, you will learn how you can use the Heron formula for quadrilaterals.
Applications and proof of Heron’s formula
With the help of explanation 12.2 and examples 5 and 6, you calculated the area of a quadrilateral. If all the sides and diagonals are givens, find the area by simply dividing the quadrilateral into equal parts. The above said can be later proven with the help of two methods – (a) Pythagoras Theorem, (b) Trigonometric Identities.
About Exercise 12.2 Class 9 Maths
In class 9 Maths Exercise 12.2, most of the questions are based on multiple figures. For example – group of triangles and rectangles, or multiple triangles. For the simplicity, we can apply Pythagoras theorem in case of right angle triangles.
However, there are only a few following applications of heron’s formula: (a) Used for calculating the area of a triangle, if the length of sides of a triangle is mentioned and (b) Used for calculating the area of a quadrilateral, if the values of sides and one diagonal is given.
Solving Exercise 12.2 using Heron’s Formula
Once you complete exercise 12.2, all 9 questions, you finally complete the chapter 12. This shall prove that you have understood the concepts of Heron’s Formula. However, a summary of the chapter is given at the end of the page which consists of two fundamental knowledge. You will use these during the solutions of exercise 12.2.
There are certain things that we suggest you to keep in mind (a) There are three different types of triangles, formally known as Equilateral, isosceles, and scalene. But Pythagoras worked for the right-angled triangles only. (b) Before using the heron formula for calculating the quadrilateral you have to divide it into triangles. (c) Heron’s formula can be used to find area of all types of triangles.