To find the area of the path formed by the two roads, we need to take into account that one road runs along the length and the other along the breadth of the rectangular plot. Both roads intersect, so we must carefully calculate the total area of the roads and subtract the overlap (intersection).

Step-by-step calculation:

1. Length of the rectangular plot (L): 825 m
2. Width of the rectangular plot (W): 375 m
3. Width of each road (both are the same): 4 cm = 0.04 m (convert to meters for consistency)

Areas to calculate:

• Area of the road along the length (A₁):
  This road has the same length as the plot (825 m) and width of 0.04 m.
  $A₁ = 825 \times 0.04 = 33 \, \text{m}^2$

• Area of the road along the breadth (A₂):
  This road has the same width as the plot (375 m) and width of 0.04 m.
  $A₂ = 375 \times 0.04 = 15 \, \text{m}^2$

• Overlap area (A₃):
  The two roads intersect at the center of the plot, and this intersection is a square with side 0.04 m. So the area of the overlap is:
  $A₃ = 0.04 \times 0.04 = 0.0016 \, \text{m}^2$

Total area of the path:

$\text{Total Area} = A₁ + A₂ - A₃$ $\text{Total Area} = 33 + 15 - 0.0016 = 47.9984 \, \text{m}^2$

So, the total area of the path is approximately 48 m².

Would you like more details or clarifications?

Here are some related questions to think about:

1. How would the area change if the width of the road were doubled?
2. What is the area of the remaining plot not covered by the roads?
3. How would the total area of the path be affected if the plot size changed?
4. Can you calculate the perimeter of the entire rectangular plot?
5. What would be the area of a circular path with the same width, running around the plot?

Tip: When calculating areas of overlapping regions, don't forget to subtract the area of the intersection!