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CBSE Case Study Questions Class 9 Maths Chapter 12 Heron’s Formula PDF Download

CBSE Case Study Questions Class 9 Maths Chapter 12  are very important to solve for your exam. Class 9 Maths Chapter 12 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  case study-based   questions for Class 9 Maths Chapter 12  Heron’s Formula

Case Study Questions Class 9 Maths Chapter 12

Case Study 1: A group of students is learning about Heron’s Formula for finding the area of a triangle. They encountered the following scenario:

Rohan and Kavya came across a triangular field in their village. They made the following observations:

• The lengths of the three sides of the triangular field are 8 meters, 12 meters, and 15 meters.
• The perimeter of the triangular field is 35 meters.

Based on this information, the students were asked to apply Heron’s Formula to find the area of the triangular field. Let’s see if you can answer the questions correctly:

MCQ Questions:

Q1. The semiperimeter of the triangular field is: (a) 8 meters (b) 12 meters (c) 15 meters (d) 17.5 meters

Answer: (d) 17.5 meters

Q2. Using Heron’s Formula, the area of the triangular field is: (a) 24 square meters (b) 30 square meters (c) 36 square meters (d) 40 square meters

Answer: (b) 30 square meters

Q3. The type of triangle formed by the sides of the field is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Answer: (c) Scalene

Q4. The length of the altitude corresponding to the side of 15 meters is: (a) 2 meters (b) 4 meters (c) 6 meters (d) 8 meters

Answer: (c) 6 meters

Q5. The lengths of the altitudes corresponding to the sides of 8 meters and 12 meters are: (a) 4 meters and 6 meters (b) 6 meters and 8 meters (c) 8 meters and 10 meters (d) 10 meters and 12 meters

Answer: (a) 4 meters and 6 meters

Case Study 2: A group of students is studying Heron’s Formula for finding the area of a triangle. They encountered the following scenario:

Neha and Mohan went on a field trip to a riverbank. They noticed a triangular piece of land that they wanted to measure and calculate its area. They made the following observations:

• Neha measured the lengths of the three sides of the triangular piece of land as 7 meters, 9 meters, and 11 meters.
• Mohan measured the lengths of the three sides of the same triangular piece of land as 10 meters, 12 meters, and 15 meters.

Based on this information, the students were asked to apply Heron’s Formula to find the area of the triangular piece of land. Let’s see if you can answer the questions correctly:

Q1. Using Neha’s measurements, the semiperimeter of the triangular piece of land is: (a) 13 meters (b) 16 meters (c) 19 meters (d) 23 meters

Answer: (c) 19 meters

Q2. Using Neha’s measurements, the area of the triangular piece of land is: (a) 24 square meters (b) 26 square meters (c) 28 square meters (d) 30 square meters

Answer: (a) 24 square meters

Q3. Using Mohan’s measurements, the semiperimeter of the triangular piece of land is: (a) 16 meters (b) 18 meters (c) 21 meters (d) 25 meters

Answer: (c) 21 meters

Q4. Using Mohan’s measurements, the area of the triangular piece of land is: (a) 40 square meters (b) 42 square meters (c) 45 square meters (d) 48 square meters

Answer: (b) 42 square meters

Q5. The measurements taken by Neha represent a triangle that is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Hope the information shed above regarding Case Study and Passage Based Questions for Case Study Questions Class 9 Maths Chapter 12 Heron’s Formula with Answers Pdf free download has been useful to an extent. If you have any other queries about Case Study Questions Class 9 Maths Chapter 12 Heron’s Formula and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible.

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CBSE Class 9 Mathematics Case Study Questions

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Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

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Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

MATHS PAAGAL HAI

All questions was easy but search ? hard questions. These questions was not comparable with cbse. It was totally wastage of time.

Where is search ? bar

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Can I have more questions without downloading the app.

I love math

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NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 12 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.

Class 9 Maths Chapter 12 Heron’s Formula NCERT Solutions

Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.

NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1

NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.2

NCERT Solutions for Class 9 Maths Chapter 12 – Topic Discussion

Below we have listed the topics that have been discussed in this chapter.

• Heron’s Formula

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Case Study Questions for Class 9 Maths Chapter 12 Herons Formula

Case study questions for class 9 maths chapter 9 areas of parallelograms and triangles, case study questions for class 9 maths chapter 6 lines and angles, case study questions for class 9 maths chapter 7 triangles, case study questions for class 9 maths chapter 5 introduction to euclid’s geometry, case study and passage based questions for class 9 maths chapter 14 statistics, case study questions for class 9 maths chapter 1 real numbers, case study questions for class 9 maths chapter 4 linear equations in two variables, case study questions for class 9 maths chapter 3 coordinate geometry, case study questions for class 9 maths chapter 15 probability, case study questions for class 9 maths chapter 13 surface area and volume, case study questions for class 9 maths chapter 10 circles, case study questions for class 9 maths chapter 9 quadrilaterals, case study questions for class 9 maths chapter 2 polynomials.

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CBSE Class 12 Maths Case Study Questions With Solutions

CBSE Class 12 Mathematics Case Study Questions are introduced this year in the updated CBSE Board Exam Pattern. According to that this year the candidates need to prepare for the case study problems along with the questions that are legacy of CBSE Board.

In Class XIIth Mathematics Case Study Questions there are problems based on Objective types of questions, Assertions and Reason, and cae based problems. These problems have the intention to examine the students' overall understanding of the subject. If you are preparing for the Maths board exam then this is the right place for you. 

Here, we have provided the complete set of CBSE class 12 maths case study questions With Solutions. These are developed by the subject matter expert. If you want to score good marks in the board papers then you should practice these Case based problems. It is absolutely free of cost. 

Download PDF CBSE Class 12 Maths Case Study From the Given links. It is in chapter wise format.

Class 12th Mathematics Important Formulas, MCQ, Case-Based, Assertion and Reason

Class 12th maths case study.

In class 12th Maths Case Study the questions are based on the real world scenarios. A passage filled with information or data is provided to the students. On the basis of that paragraph upto 5 questions are developed which should be answered by the students. To answer them they need to read the passage carefully and then pay attention to the given data to solve such questions.

These types of problems are generally known as case based questions which can be only solved by referring to the given paragraph.

Class 12 Maths Important Formulas

Knowing about the Maths Important Formulas is a crucial part of solving the Maths questions. Formulas help in solving the problems more efficiently and faster. Therefore the PDF file that we have provided here consists of all the basics and Important formulas of maths. It will help in revisions and solving the questions more accurately and easily.

Every chapter has its own topics and formulas so the PDF has been divided into chapter wise format. And if you access them from this place then you will be able to get all the formulas and other questions separately.

Class 12 Maths Assertion and Reason MCQs

Class 12th Maths Assertion and Reason MCQs PDF with Solutions are also given here. It is the most important part of Case Study Questions because scoring good marks in this section is not that much hard. If your basic concepts are clear. Because most of the time such types of questions are directly prepared by referring to the concepts.

Furthermore, the assertion and reason MCQs are solved by applying the distinct approaches. For instance, to answer these questions first candidates need to verify the Assertion (Statement) and then the reason if both are correct, then learners need to verify whether both statement and reason support each other or not.

There are a total of 5 sections in CBSE Class 12 Maths Questions Term 1. Section A contains 1 mark, Section B contains 2 marks, Section C contains 3 marks, Section D contains 4 marks and the last Section E contains 5 marks. A total of 5 questions are given in these sections.

No, In Term 1 exam there will be a total of 5 questions in each case study of class 12 maths, out of which 4 are compulsory to solve.

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Class 9 Maths Case Study Questions Chapter 14 Statistics

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Case study Questions in Class 9 Mathematics Chapter 14  are very important to solve for your exam. Class 9 Maths Chapter 14 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 Maths Case Study Questions  Chapter 14 Statistics

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 9 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Statistics Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 14 Statistics

Case Study/Passage-Based Questions

Case Study 1: The Class teacher of Class X prepares the result analysis of a student. She compares the marks of a student obtained in Class IX (2018-19) and Class X (2019-20) using the double bar graph as shown below:

(i) In which subject has the performance improved the most? (a) Maths (b) Social Science (c) Science (d) English

Ans: (a) Maths

(ii) In which subject has the performance deteriorated? (a) Maths (b) Social Science (c) Science (d) English

Ans: (d) English

(iii) In which subject is the performance at par? (a) Hindi (b) Maths (c) Science (d) English

Ans: (a) Hindi

(iv) What is the difference in Maths Subject? (a) 5 (b) 30 (c) 0 (d) 10

(v) What is the percentage of marks obtained by a student in Class X (2019-20)? (a) 60% (b) 55% (c) 54% (d) 65%

Ans: (b) 55%

Case Study 2: A Mathematics teacher asks students to collect marks of Mathematics in Half yearly exams. She instructed all the students to prepare a frequency distribution table using the data collected. Ram collected the following marks (out of 50) obtained in Mathematics by 60 students of Class IX 21, 10, 30, 22, 33, 5, 37, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 36, 18, 20, 38, 22, 44, 16, 24, 10, 27, 39, 28, 49, 29, 32, 23, 31, 21, 34, 22, 23, 36, 24, 36, 33, 47, 48, 50, 39, 20, 7, 16, 36, 45, 47, 30, 22, 17.

(i) How many students scored more than 20 but less than 30? (a) 20 (b) 21 (c) 22 (d) 23

(ii) How many students scored less than 20 marks? (a) 10 (b) 11 (c) 12 (d) 14

(iii) How many students scored more than 60% marks? (a) 20 (b) 25 (c) 26 (d) 27

(iv) What is the class size of the classes? (a) 10 (b) 5 (c) 15 (d) 20

(v) What is the class mark of the class interval 30 – 40? (a) 30 (b) 35 (c) 40 (d) 70

Case Study 3:

Anil is a Mathematics teacher in Hyderabad. After Periodic test 3, he asks students to collect the Mathematics marks of all the students of Class IX- A, B, and C. A student is able to collect marks from some students. Rekha scored least mark 6 in the class and Ram scored the highest mark 59 in the class. He prepares the frequency distribution table using the collected marks and draws Histogram using the table as shown in the adjoining figure.

(a) What is the width of the class? (i) 10 (ii) 15 (iii) 5 (iv) none of these

(b) What is the total number of students in the Histogram? (i) 50 (ii) 60 (iii) 65 (iv) none of these

(c) How many students scored 50% and above marks? (i) 19 (ii) 26 (iii) 27 (iv) none of these

(d) How many students scored less than 50% marks? (i) 19 (ii) 26 (iii) 27 (iv) none of these

(e) What is the range of the collected marks? (i) 60 (ii) 59 (iii) 53 (iv) none of these

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 14 Statistics with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Statistics Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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• NCERT Solutions
• NCERT Class 9
• NCERT 9 Maths
• Chapter 12: Herons Formula
• Exercise 12.2

NCERT Solutions for Class 9 Maths Chapter 12 - Heron's Formula Exercise 12.2

* According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 10.

The best way to understand Heron’s Formula with ease is through NCERT Solutions for Class 9 Maths Chapter 12 – Heron’s Formula Exercise 12.2 and 12.1. These exercises are designed to test your conceptual grasp of the subject.

From an educational point of view, this elementary concept is significant in various fields of study. Therefore, it is essential to have a good grasp of the concept. Another key point is that these solutions are designed by highly competent teachers with many years of relevant experience.

Therefore, NCERT Solutions is one of the best guides for studies. Important topics are presented in an easy-to-understand format. Moreover, the use of complex jargon is barred throughout the content. Furthermore, content is updated as per the prescribed CBSE syllabus.

Download PDF of NCERT Solutions for Class 9 Maths Chapter 12 – Heron’s Formula Exercise 12.2

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Access other exercise solutions of Class 9 Maths Chapter 12 – Heron’s Formula

Exercise 12.1 Solutions – 6 Questions

Access Answers of Maths NCERT Class 9 Chapter 12 – Heron’s Formula Exercise 12.2

1. A park, in the shape of a quadrilateral ABCD, has C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

First, construct a quadrilateral ABCD and join BD.

We know that

C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m

The diagram is:

Now, apply Pythagoras theorem in ΔBCD

BD 2 = BC 2 +CD 2

⇒ BD 2 = 12 2 +5 2

⇒ BD 2 = 169

⇒ BD = 13 m

Now, the area of ΔBCD = (½ ×12×5) = 30 m 2

The semi perimeter of ΔABD

(s) = (perimeter/2)

= (8+9+13)/2 m

= 30/2 m = 15 m

Using Heron’s formula,

Area of ΔABD

= 6√35 m 2 = 35.5 m 2 (approximately)

∴ The area of quadrilateral ABCD = Area of ΔBCD+Area of ΔABD

= 30 m 2 +35.5m 2 = 65.5 m 2

2. Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

First, construct a diagram with the given parameter.

Now, apply Pythagorean theorem in ΔABC,

AC 2 = AB 2 +BC 2

⇒ 5 2 = 3 2 +4 2

Thus, it can be concluded that ΔABC is a right angled at B.

So, area of ΔBCD = (½ ×3×4) = 6 cm 2

The semi perimeter of ΔACD (s) = (perimeter/2) = (5+5+4)/2 cm = 14/2 cm = 7 m

Now, using Heron’s formula,

Area of ΔACD

= 2√21 cm 2 = 9.17 cm 2 (approximately)

Area of quadrilateral ABCD = Area of ΔABC + Area of ΔACD = 6 cm 2 +9.17 cm 2 = 15.17 cm 2

3. Radha made a picture of an aeroplane with coloured paper as shown in Fig 12.15. Find the total area of the paper used.

For the triangle I section:

It is an isosceles triangle and the sides are 5 cm, 1 cm and 5 cm

Perimeter = 5+5+1 = 11 cm

So, semi perimeter = 11/2 cm = 5.5 cm

Area = √[s(s-a)(s-b)(s-c)]

= √[5.5(5.5- 5)(5.5-5)(5.5-1)] cm 2

= √[5.5×0.5×0.5×4.5] cm 2

= 0.75√11 cm 2

= 0.75 × 3.317cm 2

= 2.488cm 2 (approx)

For the quadrilateral II section:

This quadrilateral is a rectangle with length and breadth as 6.5 cm and 1 cm respectively.

∴ Area = 6.5×1 cm 2 =6.5 cm 2

For the quadrilateral III section:

It is a trapezoid with 2 sides as 1 cm each and the third side as 2 cm.

Area of the trapezoid = Area of the parallelogram + Area of the equilateral triangle

The perpendicular height of the parallelogram will be

And, the area of the equilateral triangle will be (√3/4×a 2 ) = 0.43

∴ Area of the trapezoid = 0.86+0.43 = 1.3 cm 2 (approximately).

For triangle IV and V:

These triangles are 2 congruent right angled triangles having the base as 6 cm and height 1.5 cm

Area triangles IV and V = 2×(½×6×1.5) cm 2 = 9 cm 2

So, the total area of the paper used = (2.488+6.5+1.3+9) cm 2 = 19.3 cm 2

4. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

It is given that the parallelogram and triangle have equal areas.

The sides of the triangle are given as 26 cm, 28 cm and 30 cm.

So, the perimeter = 26+28+30 = 84 cm

And its semi perimeter = 84/2 cm = 42 cm

Now, by using Heron’s formula, area of the triangle =

= √[42(42-26)(42-28)(42-30)] cm 2

= √[42×16×14×12] cm 2

Now, let the height of parallelogram be h.

As the area of parallelogram = area of the triangle,

28 cm× h = 336 cm 2

∴ h = 336/28 cm

So, the height of the parallelogram is 12 cm.

5. A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

Draw a rhombus-shaped field first with the vertices as ABCD. The diagonal AC divides the rhombus into two congruent triangles which are having equal areas. The diagram is as follows.

Consider the triangle BCD,

Its semi-perimeter = (48 + 30 + 30)/2 m = 54 m

Area of the ΔBCD

∴ Area of field = 2 × area of the ΔBCD = (2 × 432) m 2 = 864 m 2

Thus, the area of the grass field that each cow will be getting = (864/18) m 2 = 48 m 2

6. An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig.12.16), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

For each triangular piece, The semi perimeter will be

s = (50+50+20)/2 cm = 120/2 cm = 60cm

Area of the triangular piece

= √[60(60-50)(60-50)(60-20)] cm 2

= √[60×10×10×40] cm 2

= 200√6 cm 2

∴ The area of all the triangular pieces = 5 × 200√6 cm 2 = 1000√6 cm 2

7. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 12.17. How much paper of each shade has been used in it?

As the kite is in the shape of a square, its area will be

A = (½)×(diagonal) 2

Area of the kite = (½)×32×32 = 512 cm 2.

The area of shade I = Area of shade II

512/2 cm 2 = 256 cm 2

So, the total area of the paper that is required in each shade = 256 cm 2

For the triangle section (III),

The sides are given as 6 cm, 6 cm and 8 cm

Now, the semi perimeter of this isosceles triangle = (6+6+8)/2 cm = 10 cm

By using Heron’s formula, the area of the III triangular piece will be

= √[10(10-6)(10-6)(10-8)] cm 2

= √(10×4 ×4×2) cm 2

= 8√5 cm 2 = 17.92 cm 2 (approx.)

8. A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per cm 2 .

The semi perimeter of the each triangular shape = (28+9+35)/2 cm = 36 cm

By using Heron’s formula,

The area of each triangular shape will be

= 36√6 cm 2 = 88.2 cm 2

Now, the total area of 16 tiles = 16×88.2 cm 2 = 1411.2 cm 2

It is given that the polishing cost of tiles = 50 paise/cm 2

∴ The total polishing cost of the tiles = Rs. (1411.2×0.5) = Rs. 705.6

9. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

First, draw a line segment BE parallel to the line AD. Then, from B, draw a perpendicular on the line segment CD.

Now, it can be seen that the quadrilateral ABED is a parallelogram. So,

AB = ED = 10 m

AD = BE = 13 m

EC = 25-ED = 25-10 = 15 m

Now, consider the triangle BEC,

Its semi perimeter (s) = (13+14+15)/2 = 21 m

Area of ΔBEC =

We also know that the area of ΔBEC = (½)×CE×BF

84 cm 2 = (½)×15×BF

BF = (168/15) cm = 11.2 cm

So, the total area of ABED will be BF×DE i.e. 11.2×10 = 112 m 2

∴ Area of the field = 84 + 112 = 196 m 2

This formula is used to find the area of a triangle when the length of the 3 sides is the only data available.

Heron also contributed in several other ways, the most notable one being the invention of the Aeolipile. The Aeolipile was the very first steam engine.

Though it was technically a steam engine, it didn’t resemble an engine. And no practical applications could be found for this invention. It was projected as a toy and a novelty item for the ancient Greeks.

Explore other important concepts related to Heron’s Formula, learn how to solve numerical problems and more only on NCERT Solutions For Class 9 Maths – the best resources online to help you study better.

Key Features of NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Exercise 12.2

• Well-structured content
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the level is a bit up. the solutions must be easy for the kids to understand. by the way its nice its perfect as i am also a teacher it is speechless that the students can learn sitting on there bed because of you all.

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