Calculating the Area of a Gravel Path and its Construction Cost

Whether you're planning to build a path for decorative purposes or for practical reasons such as easy access to a rectangular area, understanding how to calculate its area and the associated construction cost is crucial. This article will walk you through the steps to determine these factors for a given scenario.

Problem Statement

Let's consider a scenario where you have a rectangular grassy plot with dimensions 112 meters by 78 meters. This plot includes a 2.5-meter-wide gravel path running around it on the inside. We need to calculate the area of this path and the cost of constructing it.

Understanding the Geometry

Firstly, let's visualize the plot and the gravel path within it. The grassy plot forms the outer rectangle, while the inner rectangle represents the space that is not covered by the gravel path. The gravel path forms a border of uniform width (2.5 meters) around the inner rectangle.

Calculations

Dimensions of the Outside and Inside Plots

The outside dimensions of the rectangular plot are 112 meters in length and 78 meters in breadth. Since the gravel path is 2.5 meters wide on all sides, the dimensions of the inside plot are reduced. The length of the inner plot is: 112 - 2 * 2.5 107 meters. The breadth of the inner plot is: 78 - 2 * 2.5 73 meters.

Area Calculations

The area of the outside plot can be calculated as:

Area of outside plot 112 x 78 8736 square meters.

The area of the inner plot is given by:

Area of inner plot 107 x 73 7811 square meters.

The area of the gravel path is the difference between the area of the outside plot and the inner plot:

Area of the path 8736 - 7811 925 square meters.

Construction Cost

Given the cost of construction per square meter is Rs. 120, the total cost for constructing the gravel path can be calculated as:

Total cost of construction 925 x 120 Rs. 111000.

General Formula

The area of the gravel path in a similar scenario can be calculated using the following formula:

Area of the inner rectangular plot (L - 2 * width) x (B - 2 * width), where L, B are the length and breadth of the outside plot, and width is the uniform width of the gravel path.

Total area of the path Area of the outside plot - Area of the inner rectangular plot.

Conclusion

Understanding the geometric and construction cost calculations of a gravel path not only helps in planning but also in budget management. By applying these principles, you can ensure efficient use of materials and funds while achieving the desired outcome.

For more detailed and dynamic calculations, consider using a spreadsheet or algebraic formulas to adapt to different dimensions and cost factors.