Finding the Cost of Fencing

Oct 13, 2025 by talynt.org 90 views

Finding the Cost of Fencing a Square Plot of Side 145m at the Rate of £70 per m

In this article, we will learn how to find the cost of fencing a square plot of side 145m at the rate of £70 per m. This problem involves basic geometry and arithmetic operations. We will use the formula for the perimeter of a square to find the total length of fencing required and then multiply it by the rate per meter to find the total cost.

Understanding the Problem

The problem states that we have a square plot with a side length of 145m. We need to find the cost of fencing this plot at the rate of £70 per m. To solve this problem, we need to find the perimeter of the square, which is the total length of fencing required.

Perimeter of a Square

The perimeter of a square is given by the formula:

P = 4 × s

where P is the perimeter and s is the side length.

Calculating the Perimeter

Substituting the given value of s = 145m into the formula, we get:

P = 4 × 145 P = 580m

So, the total length of fencing required is 580m.

Finding the Cost of Fencing

Now that we have the total length of fencing required, we can find the cost of fencing by multiplying it by the rate per meter:

Cost = P × Rate Cost = 580 × £70 Cost = £41,400

Therefore, the cost of fencing the square plot of side 145m at the rate of £70 per m is £41,400.

In this article, we learned how to find the cost of fencing a square plot of side 145m at the rate of £70 per m. We used the formula for the perimeter of a square to find the total length of fencing required and then multiplied it by the rate per meter to find the total cost. This problem involves basic geometry and arithmetic operations, and it is an essential concept in mathematics and real-life applications.

Real-Life Applications

This problem has many real-life applications, such as:

Finding the cost of fencing a plot of land for a new construction project
Calculating the cost of fencing a garden or a park
Determining the cost of fencing a sports field or a playground

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

Make sure to read the problem carefully and understand what is being asked
Use the formula for the perimeter of a square to find the total length of fencing required
Multiply the total length of fencing required by the rate per meter to find the total cost
Use a calculator to simplify the calculations and avoid errors

Practice Problems

Here are some practice problems to help you practice finding the cost of fencing a square plot:

Find the cost of fencing a square plot of side 120m at the rate of £60 per m
Find the cost of fencing a square plot of side 180m at the rate of £80 per m
Find the cost of fencing a square plot of side 200m at the rate of £90 per m

Solutions

Here are the solutions to the practice problems:

Find the cost of fencing a square plot of side 120m at the rate of £60 per m:

P = 4 × 120 P = 480m Cost = 480 × £60 Cost = £28,800

Find the cost of fencing a square plot of side 180m at the rate of £80 per m:

P = 4 × 180 P = 720m Cost = 720 × £80 Cost = £57,600

Find the cost of fencing a square plot of side 200m at the rate of £90 per m:

P = 4 × 200 P = 800m Cost = 800 × £90 Cost = £72,000

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

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

P = 4 × s

where P is the perimeter and s is the side length.

Q: How do I find the cost of fencing a square plot?

A: To find the cost of fencing a square plot, you need to follow these steps:

Find the perimeter of the square using the formula P = 4 × s.
Multiply the perimeter by the rate per meter to find the total cost.

Q: What is the rate per meter?

A: The rate per meter is the cost of fencing per meter. In the problem, the rate per meter is £70.

Q: Can I use this formula to find the cost of fencing a rectangle?

A: No, this formula is only applicable to squares. If you want to find the cost of fencing a rectangle, you need to find the perimeter of the rectangle using the formula P = 2 × (l + w), where l is the length and w is the width.

Q: How do I find the cost of fencing a plot with an irregular shape?

A: To find the cost of fencing a plot with an irregular shape, you need to break down the shape into smaller shapes, such as triangles, rectangles, and squares, and then find the perimeter of each shape. Finally, you can multiply the perimeter by the rate per meter to find the total cost.

Q: Can I use a calculator to simplify the calculations?

A: Yes, you can use a calculator to simplify the calculations and avoid errors.

Q: What are some real-life applications of finding the cost of fencing a square plot?

A: Some real-life applications of finding the cost of fencing a square plot include:

Finding the cost of fencing a plot of land for a new construction project
Calculating the cost of fencing a garden or a park
Determining the cost of fencing a sports field or a playground

Q: What are some tips and tricks for finding the cost of fencing a square plot?

A: Here are some tips and tricks for finding the cost of fencing a square plot:

Make sure to read the problem carefully and understand what is being asked
Use the formula for the perimeter of a square to find the total length of fencing required
Multiply the total length of fencing required by the rate per meter to find the total cost
Use a calculator to simplify the calculations and avoid errors

Q: Can I find the cost of fencing a square plot with a non-integer side length?

A: Yes, you can find the cost of fencing a square plot with a non-integer side length. However, you need to round the side length to the nearest integer to find the perimeter and then multiply it by the rate per meter to find the total cost.

Q: What is the difference between the cost of fencing a square plot and the cost of fencing a rectangle?

A: The cost of fencing a square plot and the cost of fencing a rectangle are different because the perimeter of a square is always 4 times the side length, while the perimeter of a rectangle is 2 times the sum of the length and width.

Q: Can I use this formula to find the cost of fencing a circular plot?

A: No, this formula is only applicable to squares and rectangles. If you want to find the cost of fencing a circular plot, you need to use a different formula that takes into account the radius of the circle.

In this article, we answered some frequently asked questions about finding the cost of fencing a square plot. We covered topics such as the formula for finding the perimeter of a square, how to find the cost of fencing a square plot, and some real-life applications of this concept. We also provided some tips and tricks for finding the cost of fencing a square plot and answered some common questions about this topic.