**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:

**MCQ Questions:**

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

Answer: (c) Scalene

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