NCERT Solutions for Class 9 Chapter 10 Heron’s Formula

The Heron’s Formula Class 9 NCERT Solutions provide a clear and efficient method to learn how to calculate the area of a triangle when all three side lengths are known. Chapter 10 introduces students to Heron’s Formula, which uses the semi-perimeter of a triangle to determine its area without requiring height. 

These Heron's Formula Class 9 solutions help students understand the formula step-by-step and practice different types of problems for exam preparation. With detailed explanations, students can build a strong foundation in triangle geometry. 

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

Below we have provided NCERT Solutions for Heron's Formula Class 9:

Heron's Formula Class 9 Chapter 10 Exercise 10.1 (Page No: 134)

Below are the Heron's Formula Class 9 Questions with Solutions Exercise 10.1 (Page No: 134)

1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

Solution:

Given, Side of the signal board = a Perimeter of the signal board = 3a = 180 cm ∴ a = 60 cm Semi perimeter of the signal board (s) = 3a/2 By using Heron’s formula, Area of the triangular signal board will be =

 2. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see Fig. 10.6). The advertisements yield an earning of ₹5000 per m 2 per year. A company hired one of its walls for 3 months. How much rent did it pay?

Solution:

The sides of the triangle ABC are 122 m, 22 m and 120 m respectively. Now, the perimeter will be (122+22+120) = 264 m Also, the semi perimeter (s) = 264/2 = 132 m Using Heron’s formula, Area of the triangle ==1320 m 2 We know that the rent of advertising per year = ₹ 5000 per m 2 ∴ The rent of one wall for 3 months = Rs. (1320×5000×3)/12 = Rs. 1650000

3. There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig. 10.7 ). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Solution:

It is given that the sides of the wall as 15 m, 11 m and 6 m. So, the semi perimeter of triangular wall (s) = (15+11+6)/2 m = 16 m Using Heron’s formula, Area of the message == √[16(16-15)(16-11) (16-6)] m 2 = √[16×1×5×10] m 2 = √800 m 2 = 20√2 m 2

4. Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.

Solution:

Assume the third side of the triangle to be “x”. Now, the three sides of the triangle are 18 cm, 10 cm, and “x” cm It is given that the perimeter of the triangle = 42cm So, x = 42-(18+10) cm = 14 cm ∴ The semi perimeter of triangle = 42/2 = 21 cm Using Heron’s formula, Area of the triangle, == √[21(21-18)(21-10)(21-14)] cm 2 = √[21×3×11×7] m 2 = 21√11 cm 2

5. Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.

Solution:

The ratio of the sides of the triangle are given as 12 : 17 : 25 Now, let the common ratio between the sides of the triangle be “x” ∴ The sides are 12x, 17x and 25x It is also given that the perimeter of the triangle = 540 cm 12x+17x+25x = 540 cm 54x = 540cm So, x = 10 Now, the sides of triangle are 120 cm, 170 cm, 250 cm. So, the semi perimeter of the triangle (s) = 540/2 = 270 cm Using Heron’s formula, Area of the triangle= 9000 cm 2

6. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Solution:

First, let the third side be x. It is given that the length of the equal sides is 12 cm and its perimeter is 30 cm. So, 30 = 12+12+x ∴ The length of the third side = 6 cm Thus, the semi perimeter of the isosceles triangle (s) = 30/2 cm = 15 cm Using Heron’s formula, Area of the triangle == √[15(15-12)(15-12)(15-6)] cm 2 = √[15×3×3×9] cm 2 = 9√15 cm 2

NCERT Solutions for Maths Heron's Formula Class 9 PDF

Heron's Formula Class 9 PDF includes complete solutions to all NCERT exercises from Chapter 10. This resource provides well-explained steps, solved examples, and clear reasoning behind every solution. You can revise the concept effectively and understand how Heron’s Formula is applied in different scenarios.

By using NCERT Heron's Formula Class 9 questions with solutions, you can access structured answers and reinforce your learning. The PDF is helpful for practicing Heron’s Formula Class 9 extra questions, understanding exam patterns, and preparing thoroughly with solved examples.

NCERT Solutions for Maths Heron's Formula Class 9 PDF

Heron's Formula ONE SHOT Full Chapter Class 9 Maths Chapter 10

How to Use NCERT Solutions Class 9 Chapter 10 Heron’s Formula for Exam Preparation

To prepare effectively for exams follow the given tips using the Heron’s Formula Class 9 NCERT Solutions: 

• Begin your preparation by reading the concept from the NCERT textbook. NCERT is the basic foundation for Class 9 exam preparation.

• Understand how the semi-perimeter is calculated and how Heron’s Formula is applied step-by-step. Once you understand the theory, start solving the NCERT exercises on your own before referring to the herons formula class 9 solutions​.

• Review the Heron’s Formula Class 9 extra questions with solutions to strengthen your problem-solving skills. 

• Practice triangles with different side lengths and real-life application problems to gain accuracy and confidence.

• Regular revision, formula memorization, and timed practice will help you attempt exam questions efficiently and improve your overall performance in geometry.

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