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Class 9 Maths Worksheet | Chapter: Heron’s Formula (हेरॉन का सूत्र)
Heron’s Formula – Worksheet
Total Questions: 10 Total Marks: 20
Section A: Very Short Answer / अति लघु उत्तरीय
(1 × 4 = 4 marks)
Q1. (1 mark) Write Heron’s formula for finding the area of a triangle.
त्रिभुज का क्षेत्रफल ज्ञात करने का Heron’s formula लिखिए।
Q2. (1 mark) If the sides of a triangle are \(a, b, c\), write the formula for its semi-perimeter.
यदि त्रिभुज की भुजाएँ \(a, b, c\) हों, तो उसका अर्धपरिमाप (semi-perimeter) लिखिए।
Q3. (1 mark) Can Heron’s formula be used for a right-angled triangle? (Yes / No)
क्या Heron’s formula का प्रयोग समकोण त्रिभुज के लिए किया जा सकता है? (हाँ / नहीं)
Q4. (1 mark) What quantities are required to apply Heron’s formula?
Heron’s formula लगाने के लिए किन राशियों की आवश्यकता होती है?
Section B: Short Answer / लघु उत्तरीय
(2 × 3 = 6 marks)
Q5. (2 marks) The sides of a triangle are 5 cm, 6 cm and 7 cm. Find its area using Heron’s formula.
एक त्रिभुज की भुजाएँ 5 cm, 6 cm और 7 cm हैं। Heron’s formula से उसका क्षेत्रफल ज्ञात कीजिए।
Q6. (2 marks) The perimeter of a triangle is 30 cm and its sides are 10 cm, 9 cm and 11 cm. Find the area of the triangle.
एक त्रिभुज का परिमाप 30 cm है तथा उसकी भुजाएँ 10 cm, 9 cm और 11 cm हैं। त्रिभुज का क्षेत्रफल ज्ञात कीजिए।
Q7. (2 marks) An isosceles triangle has equal sides of 13 cm and base 10 cm. Find its area using Heron’s formula.
एक समद्विबाहु त्रिभुज की बराबर भुजाएँ 13 cm हैं तथा आधार 10 cm है। Heron’s formula से क्षेत्रफल ज्ञात कीजिए।
Section C: Long Answer / दीर्घ उत्तरीय
(4 × 2 = 8 marks)
Q8. (4 marks) The sides of a triangle are 7 cm, 8 cm and 9 cm.
(i) Find the semi-perimeter
(ii) Find the area using Heron’s formula
Show all steps clearly.
एक त्रिभुज की भुजाएँ 7 cm, 8 cm और 9 cm हैं।
(i) अर्धपरिमाप ज्ञात कीजिए
(ii) Heron’s formula से क्षेत्रफल ज्ञात कीजिए
सभी चरण स्पष्ट रूप से लिखिए।
Q9. (4 marks) The sides of a triangular park are 25 m, 17 m and 18 m. If the cost of grassing is ₹5 per m², find the total cost using Heron’s formula.
एक त्रिकोणीय पार्क की भुजाएँ 25 m, 17 m और 18 m हैं। यदि घास लगाने की लागत ₹5 प्रति वर्ग मीटर है, तो कुल लागत ज्ञात कीजिए। (Heron’s formula का प्रयोग करें)
Section D: Application Based / अनुप्रयोग आधारित
(2 × 1 = 2 marks)
Q10. (2 marks) The sides of a triangle are 6 cm, 8 cm and 10 cm.
(i) Check whether it is a right-angled triangle
(ii) Find its area using Heron’s formula
एक त्रिभुज की भुजाएँ 6 cm, 8 cm और 10 cm हैं।
(i) जाँचिए कि यह समकोण त्रिभुज है या नहीं
(ii) Heron’s formula से क्षेत्रफल ज्ञात कीजिए।
Exam Pattern Insight / परीक्षा उपयोगी संकेत
- 1 mark → definition / formula / concept
- 2 marks → direct numerical application
- 4 marks → step-wise solution with accuracy
- Units (cm² / m²) लिखना अनिवार्य
💡 Important Exam & Study Tips
- Master NCERT Fundamentals: Ensure thorough familiarity with standard textbook definitions, formulas, and in-text examples before solving advanced problems.
- Step-by-Step Presentation: In board examinations, neat presentation, correct formula application, and labeled steps earn maximum step-marking.
- Practice Under Timed Conditions: Regular practice with previous years' question papers (PYQs) builds exam speed and accuracy.
📚 Related Study Materials on StudyMats
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- CBSE Class 9 Study Notes & Question Papers
- Class 9 Maths Study Notes & Question Papers
- Heron's Formula Study Notes & Question Papers
❓ Frequently Asked Questions (FAQs)
Q1: Are these solutions aligned with the latest rationalized syllabus?
Yes, all study notes and practice questions on StudyMats strictly follow the updated NCERT textbook pattern and CBSE assessment guidelines.
Q2: How can I prepare this chapter for highest marks?
Review the theory thoroughly, solve all textbook exercise questions, and repeatedly practice the high-frequency questions provided in this guide.