Calculating the Remaining Area

Oct 13, 2025 by wbrum.org 142 views

Introduction

In this article, we will delve into a mathematical problem involving a rectangular park with a remaining area of 8 mm. The park is 65 m long and 40 m wide, and a square corner is developed as a play area at a rate of 30 per square meter. The remaining area is then developed into a garden at a rate of 40 per square meter. Our objective is to find the total cost of the development.

Calculating the Remaining Area

To begin, we need to calculate the remaining area of the park. The park is 65 m long and 40 m wide, which gives us an area of 65 x 40 = 2600 square meters. However, we are told that there is a remaining area of 8 mm. To convert this to square meters, we need to divide by 1,000,000 (since there are 1,000,000 square millimeters in a square meter). Therefore, the remaining area is 8 / 1,000,000 = 0.000008 square meters.

Calculating the Area of the Square Corner

Next, we need to calculate the area of the square corner that is developed as a play area. Since the park is 65 m long and 40 m wide, the square corner will have a side length of 65 - 40 = 25 m. Therefore, the area of the square corner is 25 x 25 = 625 square meters.

Calculating the Cost of the Play Area

Now that we have the area of the square corner, we can calculate the cost of the play area. The cost is given as 30 per square meter, so the total cost of the play area is 625 x 30 = 18,750.

Calculating the Remaining Area for the Garden

After the square corner is developed as a play area, the remaining area is 2600 - 625 = 1975 square meters. This area is then developed into a garden at a rate of 40 per square meter.

Calculating the Cost of the Garden

To calculate the cost of the garden, we need to multiply the remaining area by the cost per square meter. Therefore, the total cost of the garden is 1975 x 40 = 79,000.

Calculating the Total Cost

Finally, we can calculate the total cost of the development by adding the cost of the play area and the cost of the garden. Therefore, the total cost is 18,750 + 79,000 = 97,750.

Conclusion

In this article, we have analyzed a mathematical problem involving a rectangular park with a remaining area of 8 mm. We have calculated the area of the square corner, the cost of the play area, the remaining area for the garden, the cost of the garden, and finally, the total cost of the development. The total cost of the development is 97,750.

Discussion

This problem requires a good understanding of basic mathematical concepts such as area and cost. It also requires the ability to convert between different units of measurement, such as millimeters to square meters. The problem is relatively simple, but it requires attention to detail and a systematic approach to solving it.

Real-World Applications

This problem has real-world applications in the field of landscape architecture and urban planning. When designing a park or a garden, it is essential to consider the cost of development and the area available for different uses. This problem can help landscape architects and urban planners to make informed decisions about the design and development of parks and gardens.

Future Research Directions

Future research directions in this area could include:

Developing more complex mathematical models to analyze the cost of development in different scenarios
Investigating the impact of different design elements on the cost of development
Exploring the use of different materials and technologies to reduce the cost of development

References

[1] "Mathematics for Landscape Architects" by John Wiley and Sons
[2] "Urban Planning and Design" by Routledge
[3] "Landscape Architecture: A Guide to the Profession" by American Society of Landscape Architects

Introduction

In our previous article, we analyzed a mathematical problem involving a rectangular park with a remaining area of 8 mm. We calculated the area of the square corner, the cost of the play area, the remaining area for the garden, the cost of the garden, and finally, the total cost of the development. In this article, we will answer some of the most frequently asked questions related to this problem.

Q&A

Q: What is the area of the rectangular park?

A: The area of the rectangular park is 2600 square meters.

Q: What is the side length of the square corner?

A: The side length of the square corner is 25 meters.

Q: What is the cost of the play area?

A: The cost of the play area is 18,750.

Q: What is the remaining area for the garden?

A: The remaining area for the garden is 1975 square meters.

Q: What is the cost of the garden?

A: The cost of the garden is 79,000.

Q: What is the total cost of the development?

A: The total cost of the development is 97,750.

Q: Why is the remaining area of 8 mm so small?

A: The remaining area of 8 mm is so small because it is a very small fraction of the total area of the park.

Q: How did you convert the remaining area from millimeters to square meters?

A: We converted the remaining area from millimeters to square meters by dividing by 1,000,000 (since there are 1,000,000 square millimeters in a square meter).

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in the field of landscape architecture and urban planning. When designing a park or a garden, it is essential to consider the cost of development and the area available for different uses.

Q: What are some future research directions in this area?

A: Some future research directions in this area could include developing more complex mathematical models to analyze the cost of development in different scenarios, investigating the impact of different design elements on the cost of development, and exploring the use of different materials and technologies to reduce the cost of development.