Introduction to the Problem

Suppose you have a rectangular field that measures 13 meters in length and 10 meters in width. Surrounding this field is a cement path that is 3.5 meters wide on all sides. We need to determine the area of the cement path.

Understanding the Geometry

When a cement path surrounds a rectangle, the dimensions of the total area (including the path) increase by twice the width of the path on each side. This is because the path surrounds all four sides of the field.

Step 1: Calculate the Total Dimensions of the Field and Path

The original length of the field is 13 meters. The original width of the field is 10 meters. The cement path is 3.5 meters wide on all sides.

We need to add twice the width of the path to both the length and the width of the field.

Let's calculate the total length and width:

Calculating the Total Length: Total Length 13 meters 2 * 3.5 meters 13 meters 7 meters 20 meters. Calculating the Total Width: Total Width 10 meters 2 * 3.5 meters 10 meters 7 meters 17 meters.

Calculating the Area

To find the area of the total rectangle (field plus path), we multiply the total length by the total width:

Total Area of the Rectangle 20 meters * 17 meters 340 square meters.

Next, we calculate the area of the field itself:

Area of the Field 13 meters * 10 meters 130 square meters.

The area of the cement path is the difference between the total area and the area of the field:

Area of Cement Path Total Area - Area of the Field 340 square meters - 130 square meters 210 square meters.

Conclusion

The area of the cement path surrounding the rectangular field is 210 square meters.

Additional Insights

1. The Total Area Calculation: The total area of the field and the cement path combined is 20 meters * 17 meters 340 square meters.

2. The Field Area: The area of the actual field without the cement path is 13 meters * 10 meters 130 square meters.

3. The Path Area: Finally, the area of the cement path alone is the difference between the total area and the field area, which is 340 square meters - 130 square meters 210 square meters.