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NCERT Solutions for Class 9 Maths Chapter 12 Herons Formula Ex 12.2

NCERT Solutions Class 9 Maths Chapter 12 Exercise 12.2 are created by askIITians Maths experts to help you understand how to find the area of quadrilaterals using Heron’s formula. Let us see further what kind of questions are included in this exercise and how you can solve them. 

NCERT Class 9 Maths Chapter 12 Heron’s Formula

Heron’s formula is an important formula that you all must learn by heart as it will make your calculations much easier. Heron’s formula is used to calculate the area of a triangle when the length of all its sides is given to you. 

In junior classes, you must have learned the following formula for calculating the area of a triangle: 

Area of a triangle = 1/2 × base × height

However, in practical applications, there could be a chance when you do not know the height of a triangle. For example, if you want to find the area of a triangular park, you will easily have the length of the sides of the park but finding the height of the park might not be possible. In such cases, you can use Heron’s formula and quickly find the area of the triangular park. 

Heron’s Formula:

Area of a triangle = √s(s-a)(s-b)(s-c)

Where a, b, c are the lengths of the three sides of the triangle, and 

s = Perimeter of the triangle/2 = (a+b+c)/2 

NCERT Solutions for Class 9 Maths Chapter 12 Ex 12.2 

There are two exercises in Chapter 12 with Ex 12.1 having 6 questions and Ex 12.2 having 9 questions. Exercise 12.2 is based on the application of Heron’s formula for finding areas of quadrilaterals. 

For example, consider the quadrilateral ABCD given below. You can see that this quadrilateral is made up of two triangles, triangle ABD and triangle BCD. So, if we use heron’s formula to find the areas of these two triangles and add them, we can get the area of the quadrilateral. Exercise 12.2 is based on such questions only.  

This exercise not only tests your knowledge about Heron’s formula but also checks your analytical abilities and problem-solving skills. You need to analyse how a quadrilateral can be divided into different shapes, especially triangle(s) so that you can find their area. Let us see how to solve each question of NCERT Class 9 Maths Chapter 12 Ex 12.2.

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 1

Question 1 of exercise 12.2 of Heron’s formula chapter is about finding the area of a quadrilateral whose length of four sides are given to you. Also, it is given that one of the angles of the quadrilateral is 90 degrees. This means one of the triangles is a right-angled triangle. 

You can now solve this question easily in the following steps:

  1. Find the length of the hypotenuse of the right-angled triangle. This hypotenuse is the common side of the two triangles that are forming the quadrilateral. 
  2. Calculate the area of both the triangles using Heron’s formula. 
  3. Add the areas of the triangles to find the complete area of the quadrilateral. 

You can check how to do every step given above in our NCERT Solutions for Class 9 Maths Chapter 12. We have explained every step with calculations and diagrams for your better understanding. 

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 2

Question 2 of this exercise is quite simple. In this question, you have to find the area of a quadrilateral whose lengths of all sides are given to you. It also gives you the length of the diagonal so that you can easily apply Heron’s formula and find the areas of the two triangles. Can you draw the diagram of this question? It will give you a better idea of how to solve it. Download our free NCERT solutions for this chapter and check its diagram. 

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 3

Question 3 is quite interesting but it involves a lot of calculations so make sure to stay attentive while solving it. You are given the figure of an aeroplane and you have to find its area. You can clearly see that the aeroplane figure comprises different shapes. Can you name them all? Well, it includes three triangles, one rectangle and one trapezium. 

To solve this question you can follow these steps:

  1. First, label the diagram and write the measurements of all the sides. All the lengths are already given in the diagram. 
  2. Calculate the areas of the individual figures and add them to find the area of the triangle. 

In our online NCERT Solutions for Class 9 Maths Chapter 12 Ex 12.2, we have solved this question elaborately. Every calculation is done separately so that you can understand how to solve this question. It is quite a tricky one but you must not worry, we are here to help. 

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 4

Question 4 of Class 9 Maths Chapter 12 Ex 12.2 is a little different. You have to find the height of the parallelogram. You are given that there is a triangle and a parallelogram that share the same base and have the same area. The sides of the triangle are given to you and you have to find the height of the parallelogram. How will you do that? Where will you use Heron’s formula here? Now, this question is a little twisted. You need to draw a clear diagram to understand it as we have done in our NCERT solutions. 

To solve this question, you need to do the following:

  1. Find the area of the triangle using Heron’s formula. It will also be the area of the parallelogram. 
  2. Use the formula of finding the area of the parallelogram to calculate the height of the parallelogram. 

We have provided stepwise calculations for this question. Download our NCERT solutions for Heron’s formula chapter for free and see how to solve this question. 

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 5 

The fifth question of Ex 12.2 of Heron’s formula chapter will test your analytical skills. It is given to you that 18 cows have to graze on a rhombus-shaped field. You are given the length of sides of the rhombus and the length of its longer diagonal. You have to find how much area each of the cows will be getting to graze. 

The question might seem tricky but it can be solved easily in the following steps:

  1. Draw a diagram based on the information you are given for a better understanding of the question. 
  2. Calculate the area of the rhombus by finding the area of the two triangles formed in a rhombus. 
  3. Add the areas to find the area of the rhombus. 
  4. Divide the area of the rhombus by 18 to find how much area can be covered by each cow. 

Do not forget to use the unit of area that is metre-square as per this question. If you are facing problems in solving this question, our NCERT online solutions are free to access. Check them right away!

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 6 

Question 6 of Ex 12.2 for Class 9 Maths Chapter 12 is based on a figure of an umbrella. It is given that the umbrella is made by stitching 10 pieces of triangular cloth of 2 colours together. The length of the sides of the triangular pieces is given to you. You have to find how much cloth of each colour will be required. 

Again, a question that needs problem-solving and strategic thinking. But we have deciphered it for you in the following steps:

  1. You know that there are a total of 10 cloth pieces. So, there will be 5 pieces of each colour. 
  2. If you find the area of 1 piece using Heron's formula, you can find the area of 5 pieces of one colour and you will have your answer. 

Some questions seem tricky in the beginning, but if you read them carefully, finding their solution becomes easier. If you still find this question a little tricky, don’t worry. You can check the stepwise solution in our NCERT Solutions for Chapter 12 Heron’s formula. Practice the question a few times and you will be able to tackle such tricky questions easily in the exams. 

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 7

Question 7 is an interesting question based on the application of Heron’s formula. You are given that a kite is made of a square and an isosceles triangle. The kite needs to be made of three colours. You are given the length of the diagonal of the square. You have to find how much paper of each colour is required to make the kite. 

To solve this question, just follow these steps:

  1. You must know that both the diagonals of a square are equal in length. Also, the area of a square is given by 1/2(diagonal)^2. 
  2. Find the area of the square and then divide it by 2 to find how much paper of colour I and colour II is required. 
  3. Then, use Heron’s formula to find the area of the isosceles triangle to find how much paper of colour III is needed. 

Find how to solve this question step by step in our NCERT Solutions for Class 9 Maths Chapter 12. 

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 8 

Question 8 involves complex calculations so pay attention while solving them. Just one mistake and you will end up with the wrong answer. The question includes a diagram of a floral design that includes 16 triangular tiles. The length of the sides of the triangles is given to you. You have to find the cost of polishing the tiles. 

To solve this question, you must know that the cost of polishing the tiles can be found if you know the area of the tiles. So, follow these steps to reach your answer:

  1. Find the area of one triangle using Heron’s formula. 
  2. Multiply the area with 16 to find the area of all the tiles. 
  3. Multiply the cost of polishing per centimetre square with the total area and you will have the total cost with you. 

Remember that the final answer to this question will be in rupees and not a centimetre square since you are finding the cost. Many students make such mistakes in their homework and tests and lose marks despite knowing the concept. 

NCERT Solution for Class 9 Maths Chapter 12 Ex 12.2 Question 9

The last question of this exercise tests your knowledge of geometry and how you can apply Heron’s formula. You are given the lengths of all the sides of a trapezium-shaped field and you have to find its area. The question seems simple but you need to use Heron’s formula here. So you need to divide the trapezium in such a way that a triangle is formed. 

The best method to solve this question is to form a clear, labelled diagram of the trapezium. Then you need to construct a line parallel to one of its sides and form a triangle and a parallelogram. Find their areas and add them to find the area of the trapezium. 

Don’t worry, we have solved this question step by step in our free NCERT solutions for Heron’s formula chapter. Download them today and start solving. 

Free NCERT Class 9 Maths Solutions for Chapter 12 Heron’s Formula Ex 12.2 

askIITians is an online learning platform where students find the correct study resources prepared by IITians. Our Maths team have solved all the 9 questions of Ex 12.2 for students so that one can study without any hurdles. Here are three main features of our NCERT Class 9 Maths solutions for Heron’s Formula. 

  • Free of Cost: Our NCERT solutions are available online at free of cost. Anyone can download them and study. 
  • Prepared by IITians: These solutions are prepared by our Maths team comprising graduates from the top engineering and medical colleges of India like IIT, NIT, IISc and more. 
  • Detailed Solutions: Each question is solved step-by-step so that every student can understand them without any additional help or guidance.  

NCERT Solutions for Class 9 Maths Heron’s Formula Frequently Asked Questions 

  1. How to master Heron’s Formula chapter in Class 9 Maths? 

You must understand what Heron's Formula is and how it is used. For that practice, some solved examples are given in the NCERT book. Then, you must solve every exercise question step by step. You should also practice previous year questions based on Heron’s formula to check how much you have learned. 

  1. Are there any prerequisites for this chapter? 

Yes, you must know how to find the perimeter and area of basic shapes such as triangle, square, rectangle, parallelogram, rhombus, etc. You must also have complete knowledge of the properties of these shapes. 

  1. Can Heron’s formula be used to find the area of a scalene triangle? 

Yes, Heron’s formula can be used to find the area of a scalene triangle. All you need are the lengths of its three sides. 

  1. Are askIITians NCERT solutions for Heron’s formula reliable? 

Yes, all these solutions are double-checked by our Maths faculty. We have ensured that every question has a stepwise solution. All the explanations are also mentioned clearly to help you understand how to solve every question correctly in exams. 


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