Calculating the Side of the Garden

Oct 13, 2025 by talynt.org 75 views

Introduction

In this article, we will explore the concept of calculating the area and perimeter of a garden in 225 m². We will also discuss the cost of fencing and tilling the land. The garden is in the shape of a square, and we will use the formula for the area and perimeter of a square to solve the problem.

Calculating the Side of the Garden

To calculate the side of the garden, we need to use the formula for the area of a square:

Area = side²

We are given that the area of the garden is 225 m². We can plug this value into the formula and solve for the side:

225 = side²

To solve for the side, we need to take the square root of both sides of the equation:

side = √225

side = 15 m

So, the side of the garden is 15 m.

Calculating the Perimeter of the Garden

The perimeter of a square is given by the formula:

Perimeter = 4 × side

We can plug in the value of the side we calculated earlier:

Perimeter = 4 × 15 m

Perimeter = 60 m

So, the perimeter of the garden is 60 m.

Calculating the Cost of Fencing

The cost of fencing is given as $220 per meter. We can calculate the total cost of fencing by multiplying the perimeter of the garden by the cost per meter:

Cost of fencing = Perimeter × Cost per meter

Cost of fencing = 60 m × $220/m

Cost of fencing = $13,200

So, the cost of fencing the garden is $13,200.

Calculating the Cost of Tilling the Land

The cost of tilling the land is given as $10 per square meter. We can calculate the total cost of tilling the land by multiplying the area of the garden by the cost per square meter:

Cost of tilling = Area × Cost per square meter

Cost of tilling = 225 m² × $10/m²

Cost of tilling = $2,250

So, the cost of tilling the land is $2,250.

Conclusion

In this article, we calculated the area and perimeter of a garden in 225 m². We also calculated the cost of fencing and tilling the land. The garden is in the shape of a square, and we used the formula for the area and perimeter of a square to solve the problem. We found that the side of the garden is 15 m, the perimeter is 60 m, the cost of fencing is $13,200, and the cost of tilling the land is $2,250.

Mathematical Formulas Used

Area of a square: Area = side²
Perimeter of a square: Perimeter = 4 × side
Cost of fencing: Cost of fencing = Perimeter × Cost per meter
Cost of tilling: Cost of tilling = Area × Cost per square meter

Glossary of Terms

Area: The amount of space inside a two-dimensional shape.
Perimeter: The distance around a two-dimensional shape.
Side: A straight line that forms the edge of a two-dimensional shape.
Cost per meter: The cost of fencing per meter.
Cost per square meter: The cost of tilling per square meter.

Real-World Applications

Calculating the area and perimeter of a garden can help you determine how much fencing and tilling you need to do.
Calculating the cost of fencing and tilling can help you budget for these expenses.
Understanding the formulas for the area and perimeter of a square can help you solve problems in other areas of mathematics, such as geometry and trigonometry.

Practice Problems

Calculate the area and perimeter of a garden in 400 m².
Calculate the cost of fencing a garden with a perimeter of 80 m and a cost per meter of $250.
Calculate the cost of tilling a garden with an area of 300 m² and a cost per square meter of $15.

References

[1] "Mathematics for Dummies". John Wiley & Sons. 2019.
[2] "Geometry: A Comprehensive Introduction". McGraw-Hill. 2018.
[3] "Trigonometry: A First Course". Pearson. 2017.
Q&A: Calculating the Area and Perimeter of a Garden in 225 m² ================================================================

Q: What is the formula for calculating the area of a square?

A: The formula for calculating the area of a square is:

Area = side²

Q: How do I calculate the side of a square when given the area?

A: To calculate the side of a square when given the area, you need to take the square root of both sides of the equation:

side = √Area

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

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

Perimeter = 4 × side

Q: How do I calculate the cost of fencing a garden?

A: To calculate the cost of fencing a garden, you need to multiply the perimeter of the garden by the cost per meter:

Cost of fencing = Perimeter × Cost per meter

Q: How do I calculate the cost of tilling a garden?

A: To calculate the cost of tilling a garden, you need to multiply the area of the garden by the cost per square meter:

Cost of tilling = Area × Cost per square meter

Q: What is the difference between the area and perimeter of a garden?

A: The area of a garden is the amount of space inside the garden, while the perimeter is the distance around the garden. The area is measured in square meters, while the perimeter is measured in meters.

Q: How can I use the formulas for the area and perimeter of a square to solve problems in other areas of mathematics?

A: The formulas for the area and perimeter of a square can be used to solve problems in other areas of mathematics, such as geometry and trigonometry. For example, you can use the formula for the area of a square to calculate the area of a rectangle or triangle.

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

A: Some real-world applications of calculating the area and perimeter of a garden include:

Determining how much fencing and tilling you need to do
Budgeting for the cost of fencing and tilling
Understanding the formulas for the area and perimeter of a square can help you solve problems in other areas of mathematics

Q: Can I use the formulas for the area and perimeter of a square to calculate the area and perimeter of other shapes?

A: No, the formulas for the area and perimeter of a square are specific to squares and cannot be used to calculate the area and perimeter of other shapes.

Q: What are some common mistakes to avoid when calculating the area and perimeter of a garden?

A: Some common mistakes to avoid when calculating the area and perimeter of a garden include:

Not using the correct formula for the area and perimeter of a square
Not taking the square root of both sides of the equation when calculating the side of a square
Not multiplying the perimeter by the cost per meter when calculating the cost of fencing
Not multiplying the area by the cost per square meter when calculating the cost of tilling

Q: How can I practice calculating the area and perimeter of a garden?

A: You can practice calculating the area and perimeter of a garden by using online calculators or worksheets, or by working through practice problems in a textbook or online resource.

Q: What are some resources for learning more about calculating the area and perimeter of a garden?

A: Some resources for learning more about calculating the area and perimeter of a garden include:

Online calculators and worksheets
Textbooks and online resources
Practice problems and exercises
Online tutorials and videos