Herons Formula Class 9 Important Questions Free PDF Download

Are you preparing for your Class 9 Mathematics exams and looking to ace Chapter 10, Heron’s Formula? You’re in the right place! This chapter introduces a simple yet powerful formula to calculate the area of a triangle using its side lengths, without needing the height. It’s an essential topic not only for exams but also for solving real-world geometry problems.

In this blog, we’ve compiled a list of important questions from Heron’s Formula that cover key concepts, formulas, and applications. From basic formula-based problems to real-life applications, these questions will help you strengthen your understanding and practice effectively. Whether you're revising for an exam or just brushing up on your math skills, these questions are a must-solve!

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Chapter 10 Heron’s Formula Important Questions

Glass buildings can be strengthened using iron frames. A glass structure and its iron frame are shown below

The frame consists of equal triangles. The dimensions of a triangle are shown below

1. How much area is enclosed by one triangle?

Solution:

‍s= (a+b+c)/2

s= (8+10+6)/2s= (24)/2

s= 12

Area=√12(12−8)(12−6)(12−10)​ 

Area=√12(4)(6)(2)​ 

Area=√576

Area=24m²

2. What is the area of part 1 of the frame?

a. 84 m²

b. 1680 m²

c. 3360 m² 

d. 3696 m²

Solution:

(c) 3360 m²

‍Explanation:

‍Part 1 is composed of 7 rows of triangles, each row containing 20 triangles.

Thus, the total number of triangles in Part 1 is:

Total triangles=7×20=140

Total area=Area of one triangle×Total triangles

Total area=24×140

=3360m²

3. Maintenance of the building’s exterior is done by a company. The company charges Rs 750 per square meter per month. Which of the following calculations represents the monthly maintenance charges?

a. 24 × 12

b. 750 × 24

c. 3060 × 750

d. 6720 × 750 

Solution:(c) 3060 x 750

Explanation:

Total area of Part 1 = 3360 m²

Rate per square meter = Rs 750 per m²

Monthly charges=Total area×Rate per square meter

Monthly charges=3360×750

Chapter 10 Heron’s Formula Important Concepts

Heron’s formula is a way to find the area of a triangle when you know the lengths of all three sides. You don’t need to know the height of the triangle for this formula, which makes it very useful in certain situations.

The formula to calculate the area of a triangle is:

Area=√s(s−a)(s−b)(s−c)​

Here:

• a, b, and c are the lengths of the three sides of the triangle.
• s is the semi-perimeter of the triangle, which is calculated as:

s= (a+b+c)/2

Steps to Use Heron’s Formula

• Find the semi-perimeter (s) of the triangle using the formula s= (a+b+c)/2
• Use the side lengths (a, b, and c) and the value of s in the formula Area=√s(s−a)(s−b)(s−c)​ to calculate the area.
• Simplify the expression under the square root carefully to find the area.

Applications

Heron’s formula can be used to:

• Find the area of triangles with known side lengths.
• Solve problems involving irregularly shaped plots of land or triangular areas in geometry.

Extension

Heron’s formula can also be applied to find the areas of quadrilaterals if they can be divided into two triangles.

Key Points

• The formula works for all types of triangles (scalene, isosceles, equilateral).
• Accurate calculations require proper simplification of the square root.

Chapter 10 Heron’s Formula Important Questions: Why

When it comes to preparing for the Class 9 CBSE Mathematics exam, Chapter 10, Heron’s Formula, plays a crucial role. Here’s why solving important questions from this chapter is essential:

Exam Relevance

Heron’s Formula is a frequently asked topic in exams. Questions from this chapter often appear in the form of direct calculations, word problems, or real-life applications. Practising important questions ensures you're ready to tackle any question format confidently.

Builds Problem-Solving Skills

This chapter helps develop logical thinking and problem-solving skills. By solving a variety of questions, you’ll learn how to approach different triangle configurations and apply the formula effectively.

Strengthens Core Geometry Concepts

Heron’s Formula combines geometry with algebra, reinforcing foundational concepts like perimeter, semi-perimeter, and area. Regular practice will deepen your understanding of these concepts and their applications.

Real-world Applications

The formula is not just theoretical—it’s widely used in fields like construction, design, and land measurement. Solving questions will help you appreciate its practical importance and real-world relevance.

Boosts Confidence

Mastering Heron’s Formula through consistent practice boosts your confidence in handling both easy and challenging problems. It prepares you to score full marks in related questions.

By focusing on important questions, you’re not just preparing for exams—you’re building a solid mathematical foundation that will benefit you in higher studies and beyond. Let’s start practising to make this chapter your stronghold! We hope that you practice the above Class 9 Herons Formula Extra Questions PDF and achieve your dream marks.

All the Best!