Formula for Area of Rectangle

Oct 13, 2025 by thesweetdesigns.com 54 views

Introduction

In this problem, we are given a rectangle formed by two identical squares side by side. The area of the rectangle is given as 388cm. We need to find the perimeter of one square. To solve this problem, we will use the concept of area and perimeter of a rectangle and a square.

Understanding the Problem

Let's assume that the side length of each square is 'x' cm. Since the two squares are identical, the width of the rectangle is 'x' cm and the length of the rectangle is also 'x' cm. The area of the rectangle is given as 388cm, which is equal to the product of its width and length.

Formula for Area of Rectangle

The formula for the area of a rectangle is:

Area = Length × Width

In this case, the area of the rectangle is 388cm, and the length and width are both 'x' cm. So, we can write the equation as:

x × x = 388

Simplifying the Equation

Simplifying the equation, we get:

x^2 = 388

Finding the Value of x

To find the value of 'x', we need to take the square root of both sides of the equation:

x = √388

Calculating the Square Root

Calculating the square root of 388, we get:

x ≈ 19.73

Finding the Perimeter of One Square

Now that we have the value of 'x', we can find the perimeter of one square. The formula for the perimeter of a square is:

Perimeter = 4 × Side Length

In this case, the side length of the square is 'x' cm. So, we can write the equation as:

Perimeter = 4 × 19.73

Calculating the Perimeter

Calculating the perimeter, we get:

Perimeter ≈ 79.12

Conclusion

In this problem, we were given a rectangle formed by two identical squares side by side. The area of the rectangle was given as 388cm. We used the concept of area and perimeter of a rectangle and a square to find the perimeter of one square. We first found the value of 'x' by taking the square root of the area of the rectangle. Then, we used the value of 'x' to find the perimeter of one square.

Formula for Perimeter of Square

The formula for the perimeter of a square is:

Perimeter = 4 × Side Length

Formula for Area of Square

The formula for the area of a square is:

Area = Side Length^2

Relationship Between Area and Perimeter of Square

The area and perimeter of a square are related by the following equation:

Perimeter = 4 × √(Area)

Example

Let's consider an example where the area of a square is 400cm^2. We can find the perimeter of the square using the formula:

Perimeter = 4 × √(400)

Calculating the Perimeter

Calculating the perimeter, we get:

Perimeter = 4 × 20

Perimeter = 80

Conclusion

In this example, we found the perimeter of a square with an area of 400cm^2. We used the formula for the perimeter of a square to find the answer.

Real-World Applications

The concept of area and perimeter of a square has many real-world applications. For example, in architecture, the area and perimeter of a square are used to design buildings and structures. In engineering, the area and perimeter of a square are used to design bridges and other infrastructure.

Conclusion

In this problem, we used the concept of area and perimeter of a rectangle and a square to find the perimeter of one square. We first found the value of 'x' by taking the square root of the area of the rectangle. Then, we used the value of 'x' to find the perimeter of one square. The formula for the perimeter of a square is:

Perimeter = 4 × Side Length

The formula for the area of a square is:

Area = Side Length^2

The area and perimeter of a square are related by the following equation:

Perimeter = 4 × √(Area)

This problem has many real-world applications, and the concept of area and perimeter of a square is used in various fields such as architecture and engineering.

Final Answer

The final answer is 79.12.

Introduction

Understanding the Problem

Formula for Area of Rectangle

The formula for the area of a rectangle is:

Area = Length × Width

In this case, the area of the rectangle is 388cm, and the length and width are both 'x' cm. So, we can write the equation as:

x × x = 388

Simplifying the Equation

Simplifying the equation, we get:

x^2 = 388

Finding the Value of x

To find the value of 'x', we need to take the square root of both sides of the equation:

x = √388

Calculating the Square Root

Calculating the square root of 388, we get:

x ≈ 19.73

Finding the Perimeter of One Square

Now that we have the value of 'x', we can find the perimeter of one square. The formula for the perimeter of a square is:

Perimeter = 4 × Side Length

In this case, the side length of the square is 'x' cm. So, we can write the equation as:

Perimeter = 4 × 19.73

Calculating the Perimeter

Calculating the perimeter, we get:

Perimeter ≈ 79.12

Q&A

Q: What is the formula for the area of a rectangle?

A: The formula for the area of a rectangle is:

Area = Length × Width

Q: What is the formula for the perimeter of a square?

A: The formula for the perimeter of a square is:

Perimeter = 4 × Side Length

Q: How do you find the value of 'x' in the equation x^2 = 388?

A: To find the value of 'x', you need to take the square root of both sides of the equation:

x = √388

Q: What is the relationship between the area and perimeter of a square?

A: The area and perimeter of a square are related by the following equation:

Perimeter = 4 × √(Area)

Q: Can you give an example of how to use the formula for the perimeter of a square?

A: Let's consider an example where the area of a square is 400cm^2. We can find the perimeter of the square using the formula:

Perimeter = 4 × √(400)

Calculating the perimeter, we get:

Perimeter = 4 × 20

Perimeter = 80

Q: What are some real-world applications of the concept of area and perimeter of a square?

A: The concept of area and perimeter of a square has many real-world applications. For example, in architecture, the area and perimeter of a square are used to design buildings and structures. In engineering, the area and perimeter of a square are used to design bridges and other infrastructure.

Q: How do you find the perimeter of a square when you are given the area?

A: To find the perimeter of a square when you are given the area, you can use the formula:

Perimeter = 4 × √(Area)

Q: Can you give an example of how to use the formula for the perimeter of a square when you are given the area?

A: Let's consider an example where the area of a square is 400cm^2. We can find the perimeter of the square using the formula:

Perimeter = 4 × √(400)

Calculating the perimeter, we get:

Perimeter = 4 × 20

Perimeter = 80

Q: What is the final answer to the problem?

A: The final answer to the problem is 79.12.

Q: Can you summarize the steps to solve the problem?

A: To solve the problem, you need to follow these steps:

Write the equation x^2 = 388
Take the square root of both sides of the equation to find the value of 'x'
Use the value of 'x' to find the perimeter of one square using the formula Perimeter = 4 × Side Length

Q: What are some common mistakes to avoid when solving the problem?

A: Some common mistakes to avoid when solving the problem include:

Not taking the square root of both sides of the equation
Not using the correct formula for the perimeter of a square
Not checking the units of the answer

Q: Can you give some tips for solving the problem?

A: Some tips for solving the problem include:

Make sure to write the equation x^2 = 388 correctly
Take the square root of both sides of the equation carefully
Use the correct formula for the perimeter of a square
Check the units of the answer to make sure it is correct.