NCERT Solutions for Class 9 Maths Exercise 10.1 Heron’s Formula in Hindi and English Medium updated for session 2024-25. Get here the revised question answers and solutions of 9th Maths ex. 10.1 based on the revised syllabus and new NCERT textbooks for CBSE 2024-25.

Class: 9 | Mathematics |

Chapter 10: | Exercise 10.1 |

Chapter Name: | Heron’s Formula |

Content: | NCERT Textbook Solution |

Mode of Solution: | Text and Videos format |

Session: | CBSE 2024-25 |

Medium: | Hindi and English Medium |

### NCERT Solutions for Class 9 Maths Exercise 10.1

Class 9 Maths Exercise 10.1 contains only 6 questions based on Heron’s formula. The PDF and video solutions of exercise are in Hindi and English to download. If student feel difficulty in understanding through PDF, please see the video solutions for better learning.

### Area of Triangles with Heron’s Formula

Heron’s Formula is applied in the calculations of the area of a triangle. In the previous chapter of NCERT Solutions for Mathematics class 9, you have studied the different shapes. We have already studied the ways to find areas of squares, circles, triangles, and quadrilaterals along with their properties.

This is why you should have a well-versed knowledge of the area and perimeters of different shapes mainly triangles. Initially, you know that we can find the area of triangle using Pythagoras formula but still have limitations. What if you calculate the area of the triangle, not just one type of triangle multiple types of triangles.

#### Introduction to Heron’s contributions

Though it is mentioned as 10 AD (After Christ was born) but many believe it is not fully accurate. Different translations give different dates but are somewhere near to each other. For this reason, it is highly unlikely to give up a date for his period of life. Since the origin of Heron de Alejandria is so old that the records are not fully available.

This is the only reason why most of the establishments of this great Mathematician remain a mystery to us. Scholars and historian have their theory that Heron did not publish any work. He was later than Archimedes, who was a famous engineer, physicist, and inventor, but he is a different story for later.

##### Heron’s contribution towards studies

Nothing is much clearer about the life of Heron, but what we really know about the contribution that he made in the area of education.

It is not just in Mathematics, he contributed only, researchers say he published his first work of cybernetics. Though it is not formalized as the field of education until 20th century. Along with it is mentioned in 13 books among which the most famous is Metrica.

###### Heron’s Formula for Geometry

Heron is among some of the greatest of all time, whose work is still we’re using to calculate the area of triangles. When the three sides of triangles are given, we just think about Heron’s formula geometry.

Unlike the famous Pythagorean Theorem, it is applicable in all types of triangles as long as the sides are given. Even in some cases, you can use it for the quadrilateral and polygons. As per the exercise 10.1 the formula for the Area of Triangle = √(s (s-a)(s-b)(s-c)).

### What do we explore in class 9 exercise 10.1 Heron’s formula?

Class 9 students study exercise 10.1 of Maths in order to gain an understanding of the principles of calculating areas numerically. Heron’s formula is a mathematical formula that can be used to find the area of a triangle when all three sides are known. By understanding Heron’s formula, we can calculate the area of a triangle easily. Students will gain a better understanding of how geometry works and how shapes and angles can be used to solve problems.

### What is the scope of heron’s Formula in exercise 10.1 of 9th Maths?

Heron’s Formula is a trick or formula that is used to calculate the area of a triangle when the lengths of all three sides are known. It can be used in a variety of applications in class 9 Maths like finding area of triangles, quadrilateral and any other polygons.

### How to prepare exercise 10.1 in class 9 Maths exams?

Class 9 Maths exercise 10.1 is based on Heron’s formula. It is a mathematical condition or trick that is used to calculate the area of a triangle if three side lengths are known.

We can begin by introducing the concept of a triangle. Explain that a triangle is a three-sided shape that has three angles and three sides. Next, know the functionality of Heron’s formula that can be used to calculate the area of a triangle.

Area = √(s(s-a)(s-b)(s-c))

Where a, b and c are the sides of the triangle, and s is the semi-perimeter, which is equal to (a + b + c)/2.

At the end, implement the formula to calculate the area of a triangle. Practice by calculating the area of a given triangle taking different kinds of triangle.