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

Everyone already knows how to find the area of a triangle using the general formula or the specific formula for an Equilateral triangle. But have you ever wondered how we can get the area of a triangle when it is a scalene triangle, which means the length of all three sides is different, and you have no clue how to get the altitude? In such cases, Heron’s formula becomes a lifesaver, helping us find the triangle's area. In Class 9 Maths Chapter 10 solutions, students will learn about Heron’s formula, also known as the Heron’s formula. Heron’s formulas have many real-life examples, and they help calculate the area of irregular plots. The NCERT Solutions for this chapter simplify the process through practical questions and straightforward explanations.

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This Story also Contains

1. Heron's Formula Class 9 Questions And Answers PDF Free Download
2. Herons Formula Class 9 Solutions - Important Formulae
3. NCERT Solutions for Class 9 Maths Chapter 10: Exercise Questions
4. Class 9 Maths NCERT Chapter 10: Extra Question
5. Approach to Solve Questions of Heron's Formula Class 9
6. NCERT Solutions for Class 9 Mathematics: Chapter-wise
7. NCERT solutions for class 9, Subject-Wise
8. NCERT Books and NCERT Syllabus

The concept of Heron’s formula is not only important for class 9 board exams but also for higher-level and competitive exams. These Heron’s formula class 9 NCERT solutions follow the latest CBSE guidelines and have been prepared by Careers360 teachers who have multiple years of experience in this field. Students can try to solve the exercises of the NCERT textbooks on their own before checking these well-structured solutions of Heron’s formula class 9. The latest NCERT Solutions for Class 9 Maths covers various triangle types and extends the concept to real-world problems involving quadrilaterals. Along with this, the NCERT Solutions for Class 9 materials help students apply the formula accurately, especially when dealing with application-based or word problems in exams.

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

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Herons Formula Class 9 Solutions - Important Formulae

Triangle:

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.

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 cm, b = 10 cm, c = 17 cm

$s=\frac{a+b+c}{2}=\frac{9+10+17}{2}=\frac{36}{2}=18cm$

$\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{18(18-9)(18-10)(18-17)}$

$=\sqrt{18\times 9\times 8\times 1}=\sqrt{1296}=36c{m}^2$

Approach to Solve Questions of Heron's Formula Class 9

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

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