To find the total area used as path, we need to calculate the area of the two cross paths in the grassy plot. The two paths intersect at right angles, so we need to account for both their individual areas and the area where they overlap.

Step 1: Calculate the area of each path

Each path is 4 meters wide. One path is parallel to the length (80 m) and the other is parallel to the width (60 m).

1. Area of the path parallel to the length:

   • This path has a width of 4 meters and a length of 80 meters. $\text{Area of first path} = 80 \, \text{m} \times 4 \, \text{m} = 320 \, \text{m}^2$

2. Area of the path parallel to the width:

   • This path has a width of 4 meters and a length of 60 meters. $\text{Area of second path} = 60 \, \text{m} \times 4 \, \text{m} = 240 \, \text{m}^2$

Step 2: Subtract the overlapping area

The two paths intersect at the center of the field, and the area where they overlap has been counted twice (once for each path). This overlapping area is a square with side 4 meters (the width of each path).

$\text{Area of overlap} = 4 \, \text{m} \times 4 \, \text{m} = 16 \, \text{m}^2$

Step 3: Calculate the total area of the paths

Now, we can calculate the total area used as path by adding the areas of both paths and subtracting the overlap:

$\text{Total area of path} = 320 \, \text{m}^2 + 240 \, \text{m}^2 - 16 \, \text{m}^2 = 544 \, \text{m}^2$

Final Answer:

The total area used as path is 544 square meters.

Would you like further details on this solution? Here are a few related questions that might interest you:

1. How would the total area change if the paths were 5 meters wide instead of 4 meters?
2. What would happen if the paths were not perpendicular but still intersected at the center?
3. How would the total area of paths change if the field's dimensions were increased?
4. What is the total area of the grassy plot that is left after the paths are constructed?
5. Can you calculate the total perimeter of the paths?

Tip: Always be cautious when counting overlapping areas in geometric problems; it's easy to double-count shared regions like the intersection of paths.