The correct answer is option (B):
525 sq.m.
Let's break down how to solve this problem. We have a rectangular plot of land, and we're building two roads across it, creating a crossroads. The key is understanding how the roads intersect and how to avoid double-counting the area where they overlap.
The plot of land is 45m by 65m. The roads are perpendicular and 5m wide. Imagine the roads as a plus sign (+) crossing the plot.
1. **Calculate the area of the roads individually:**
* One road will run along the 45m side, and its area is 45m * 5m = 225 sq.m.
* The other road will run along the 65m side, and its area is 65m * 5m = 325 sq.m.
2. **Identify the overlap:**
* The two roads intersect, forming a square. The dimensions of this square are determined by the width of the roads, which is 5m * 5m = 25 sq.m. The intersecting roads cover the same land space.
3. **Calculate the total area of the crossroads:**
* To get the total area covered by the roads, you might initially think to add the areas of the two roads (225 sq.m + 325 sq.m = 550 sq.m). However, this would double-count the area of intersection. We've accounted for the intersecting space twice, so we need to subtract the area of the overlap:
* Total Area of Roads = Area of road 1 + Area of road 2 - Area of intersection = 225 sq.m. + 325 sq.m. - 25 sq.m. = 525 sq.m.
Therefore, the area of the crossroads is 525 sq.m.