Question:
Class 9th exercise 12.2 question no. 8 Related: Ex 12.1 NCERT Solutions- Heron’s Formula? Explain in details.

Answer:

Introduction:
In this question, we are asked to find the area of a triangle using Heron's Formula. To solve this question, we need to understand what Heron's Formula is and how it can be applied to find the area of a triangle.

Heron's Formula:
Heron's Formula is a formula used to find the area of a triangle when the lengths of its three sides are known. The formula is given as:

Area = √(s(s-a)(s-b)(s-c))

Where,
- Area is the area of the triangle.
- s is the semi-perimeter of the triangle, which is calculated as (a+b+c)/2, where a, b, and c are the lengths of the three sides of the triangle.
- a, b, and c are the lengths of the three sides of the triangle.

Steps to solve the question:
To find the area of the given triangle using Heron's Formula, follow these steps:

1. Identify the lengths of the three sides of the triangle.
2. Calculate the semi-perimeter (s) using the formula (a+b+c)/2, where a, b, and c are the lengths of the three sides.
3. Substitute the values of s, a, b, and c into the Heron's Formula.
4. Simplify the expression inside the square root.
5. Take the square root of the simplified expression to find the area of the triangle.

Example:
Let's take an example to understand how to apply Heron's Formula.

Question: Find the area of a triangle with sides of length 5 cm, 6 cm, and 7 cm.

Solution:
Step 1: Identify the lengths of the three sides of the triangle: a = 5 cm, b = 6 cm, c = 7 cm.

Step 2: Calculate the semi-perimeter (s) using the formula (a+b+c)/2:
s = (5 + 6 + 7)/2 = 18/2 = 9 cm.

Step 3: Substitute the values of s, a, b, and c into the Heron's Formula:
Area = √(9(9-5)(9-6)(9-7)).

Step 4: Simplify the expression inside the square root:
Area = √(9(4)(3)(2)) = √(216).

Step 5: Take the square root of the simplified expression to find the area of the triangle:
Area = √216 = 14.6969 cm² (approx).

Therefore, the area of the triangle is approximately 14.6969 cm².

Conclusion:
Heron's Formula is a useful formula for finding the area of a triangle when the lengths of its three sides are known. By following the steps mentioned above, we can easily calculate the area of a triangle using Heron's Formula.