Understanding Perimeter and Area of a Square Field through Ramesh’s Example

The concept of a square field and its properties such as perimeter and area can be better understood through a simple example. In this article, we will explore how Ramesh's activity of covering 60 meters in two rounds of a square field can help us determine the perimeter and area of the field. We will break down the problem step by step, illustrating the calculations and providing further examples for better understanding.

Problem Statement

Ramesh has completed two rounds of a square field, covering a distance of 60 meters. The task is to find the perimeter and the area of the field based on this information.

Step-by-Step Solution

Step 1: Determine the Perimeter

Given that Ramesh has completed two rounds of the field and covered a total distance of 60 meters, we can find the perimeter of one round.

Distance for one round:
60 meters div; 2 30 meters

Thus, the perimeter of the square field is 30 meters.

Step 2: Calculate the Length of One Side of the Square

Now that we know the perimeter of the square field, we can find the length of one side of the square.

Length of one side:
Perimeter divide; 4 30 meters divide; 4 7.5 meters

Therefore, each side of the square field measures 7.5 meters.

Step 3: Determine the Area of the Square

To find the area of the square field, we need to square the length of one side of the square.

Area of the square:
Length of one side times; Length of one side 7.5 meters times; 7.5 meters 56.25 square meters

Thus, the area of the square field is 56.25 square meters.

Related Concepts and Examples

Concept of Perimeter and Area

The perimeter of a square is the total distance around the square, and the area is the measure of the space inside the square. Understanding these concepts is crucial in various practical applications such as construction, gardening, and land measurement.

Let's consider another example for additional clarity. If the perimeter of a square field is 50 meters, we can calculate the length of one side and the area of the field:

Length of one side:
50 meters divide; 4 12.5 meters

Area of the square:
12.5 meters times; 12.5 meters 156.25 square meters

Practice Problems

Problem 1

A square field has a perimeter of 80 meters. What is the length of one side of the square, and what is the area of the field?

Length of one side:
80 meters divide; 4 20 meters

Area of the square:
20 meters times; 20 meters 400 square meters

Problem 2

Given a square field with an area of 144 square meters, what is the length of each side, and what is the perimeter of the field?

Length of one side:
radic;144 meters 12 meters

Perimeter of the square:
12 meters times; 4 48 meters

Conclusion

In summary, by understanding the relationship between the perimeter and area of a square field, we can easily solve problems using simple mathematical calculations. Whether it is a 60-meter distance for two rounds or a general perimeter, the steps involved in calculating the length of the sides and the area remain consistent. This knowledge is valuable in many practical fields such as surveying, architecture, and landscaping.