NCERT Solutions for Class 9 Maths Chapter 10 Heron's Formula

In the world of triangles, Heron's Formula is the golden key to the unknown space within the triangle(s). Everyone knows their own ways of finding the area of a triangle as intended, either through the general area triangle formula or the specially intended formula for an Equilateral triangle. Did you ever stop and ask yourself how you would find the area of a triangle if it were of a scalene nature (different lengths for all three sides), and you had zero idea how to find an altitude? That's where we turn to Heron's formula, and it helps us find the triangle's area. Heron's formula can be used in the actual world, and they can help us to figure out the area of irregular plots. This NCERT solutions chapter effectively breaks it down with real examples of questions and makes it understandable.

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This Story also Contains

1. Heron's Formula Class 9 Questions And Answers PDF Free Download
2. NCERT Solutions for Class 9 Maths Chapter 10: Exercise Questions
3. Class 9 Maths NCERT Chapter 10: Extra Question
4. Heron's Formula Class 9 Chapter 10: Topics
5. Heron's Formula Class 9 Solutions - Important Formulae
6. Approach to Solve Questions of Heron's Formula Class 9
7. NCERT Solutions for Class 9 Mathematics: Chapter-wise

Heron’s formula is the poet's way of determining the area of a triangle. Heron's formula is not just important for grade 9 board exams, but also for higher grade tests and competitive exams as well. These Heron's formula class 9 NCERT solutions align with the current guidelines by CBSE for study, and they have been developed by Careers360 teachers with many years of experience in this area. Students can make an effort to solve the exercises in the NCERT textbooks on their own before validating their answers with the well-constructed solutions in Heron's formula class 9. The most current NCERT solutions for Class 9 Maths not only deal with different types of triangles, but they also take the concept further to quadrilateral problem situations in the real world. An added benefit of the NCERT Solutions for Class 9 materials is to help students apply the formula correctly, especially under test conditions, although the application-based or word problems can also become test questions.

Heron's Formula Class 9 Questions And Answers PDF Free Download

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NCERT Solutions for Class 9 Maths Chapter 10: Exercise Questions

Class 9 Maths NCERT Chapter 10: Extra Question

Question: Find the area of a triangle whose sides are 9 cm, 10 cm, and 17 cm using Heron’s formula.

Answer:

Let the sides be $a=9\mathrm{cm},b=10\mathrm{cm},c=17\mathrm{cm}$

$\begin{array}{rl}& s=\frac{a+b+c}{2}=\frac{9+10+17}{2}=\frac{36}{2}=18\mathrm{cm}\\ & \text{ Area }=\sqrt{s(s-a)(s-b)(s-c)}\\ & =\sqrt{18(18-9)(18-10)(18-17)}\\ & =\sqrt{18\times 9\times 8\times 1}=\sqrt{1296}=36{\mathrm{cm}}^2\end{array}$

Heron's Formula Class 9 Chapter 10: Topics

The topics discussed in the NCERT Solutions for class 9, chapter 10, Heron's Formula, are:

• Area of a Triangle — by Heron’s Formula
• Summary

Heron's Formula Class 9 Solutions - Important Formulae

Triangle:

$\text{ Semi-perimeter of a triangle }=s=\frac{(a+b+c)}{2}$

Where ' s ' is the semi-perimeter, and ' a ', ' b ', and ' c ' are the lengths of its sides.
Area $=\sqrt{s(s-a)(s-b)(s-c)}$Equilateral Triangle:

For an equilateral triangle with side length 'a':

• Its perimeter is given by: Perimeter = 3a units.

• The altitude (height) of an equilateral triangle is equal to$\frac{\sqrt{3}}{2}$ times its side length.
  Altitude $=\frac{\sqrt{3}}{2}\times a$ units.

• The area of an equilateral triangle is equal to $\frac{\sqrt{3}}{4}$ times the square of its side length,
  Area $=\frac{\sqrt{3}}{4}\times a^2$ units. These formulas are specific to equilateral triangles and are based on their unique properties.

Approach to Solve Questions of Heron's Formula Class 9

These steps will assist students in confidently handling NCERT Class 9 Heron's Formula questions.

1. Memorise the Heron’s Formula: Students need to remember the standard formula, which states Area equals the square root of semi-perimeter times its difference with each side. The formula uses "s" to denote the semi-perimeter of a triangle.

2. Calculate semi-perimeter accurately: The calculation of $s=\frac{a+b+c}{2}$ requires utmost attention because even minor errors can create problems throughout the problem-solving process.

3. Check if a triangle is valid: The triangle inequality rule should be used to verify triangle feasibility before you implement the formula.

4. Work with different triangle types: Apply Heron’s formula on various triangle shapes, including scalene, isosceles and right-angled to enhance your understanding of the concept.

5. Special attention must be given when simplifying square roots: Preparing the value inside the square root for calculation before extracting the root will reduce errors, particularly when working with irrational numbers.

6. Extend to real-world problems: When solving problems about land plots or uneven quadrilaterals, apply Heron’s rule by dividing the shape into two triangles.

NCERT Solutions for Class 9 Mathematics: Chapter-wise

We at Careers360 compiled all the NCERT class 9 Maths solutions in one place for easy student reference. The following links will allow you to access them.

NCERT solutions for class 9, Subject-Wise

Students can also check these subject-wise solutions. These solutions have explained every step and are written in very easy language.

NCERT Books and NCERT Syllabus

The following links can be used to find the latest CBSE syllabus and a reference math book. These are very useful study materials to do well in the exam.

• NCERT Books Class 9 Maths

• NCERT Syllabus Class 9 Maths

• NCERT Books Class 9

• NCERT Syllabus Class 9