A rectangular plot of land measures 50 meters by 30 meters. A circular garden with a radius of 10 meters is planted in the center. What is the area of the plot not occupied by the garden? - Abbey Badges
Optimizing Your Garden Space: Calculating the Unoccupied Area of a Rectangular Plot with a Central Circular Garden
Optimizing Your Garden Space: Calculating the Unoccupied Area of a Rectangular Plot with a Central Circular Garden
If you’re planning to design a garden, landscaping project, or even residential development on a rectangular plot, understanding the usable space is essential. Let’s explore a practical example: a rectangular plot measuring 50 meters by 30 meters with a circular garden of radius 10 meters centered in the plot. This guide explains how to calculate the unoccupied area and why spatial efficiency matters.
The Plot Dimensions
The total area of the rectangular plot is calculated using the basic formula:
Area = length × width
For this plot:
50 meters × 30 meters = 1,500 square meters
Understanding the Context
The Circular Garden
The garden is circular with a radius of 10 meters. The area of a circle is:
Area = π × r²
Where r = 10 meters.
So, the garden area is:
π × (10)² = 100π ≈ 314.16 square meters (using π ≈ 3.1416)
Calculating the Unoccupied Area
Subtract the garden area from the total plot area to find the usable ground:
Unoccupied Area = Total Area – Circular Garden Area
Unoccupied Area ≈ 1,500 – 314.16 = 1,185.84 square meters
Why This Matters
Knowing the unoccupied area helps with:
- Planning additional planting or hardscaping zones
- Ensuring proper spacing and accessibility
- Estimating water, soil, and maintenance needs
- Making informed decisions on expanding future projects
Conclusion
A rectangular plot of 50 meters by 30 meters offers a total area of 1,500 m², while the central circular garden of 10-meter radius occupies about 314.16 m². This leaves approximately 1,185.84 m² available for your landscaping, construction, or gardening plans. Efficient space planning ensures your outdoor project is both beautiful and functional.
Key Insights
Use this calculation to optimize your land use—whether you're planting native flowers, installing a water feature, or developing a sustainable garden. Accurate area measurements are the foundation of every successful design!
Keywords: rectangular plot area, circular garden area, usable space calculation, land use planning, garden area, 50m by 30m plot, circular garden garden, outdoor space optimization.
