Area of path 1= 75×2 =150sq. mArea of path 2= 50×2 =100sq. m overlapped area in between = 2×2sq. m =4sq. m Now, Total area of path=(150+100)-4sq. m = 250-4sq. m =246sq. m (ans.) IS IT CORRECT OR WRONG.

The Problem:

The problem states that there are two crossroads, each 2 meters wide, intersecting each other at right angles through the center of a rectangular area. The dimensions of the rectangle are given as 75 meters by 50 meters. The crossroads run parallel to the sides of the rectangle. We are required to find the area of the crossroads.

Understanding the Problem:

To solve this problem, we need to determine the area of the crossroads that intersect the rectangular area. The crossroads are essentially rectangular strips within the larger rectangle. We can calculate the area of these strips and subtract it from the total area of the rectangular area to find the area of the crossroads.

Solution:

Let's break down the solution into smaller steps:

Step 1: Calculate the area of the rectangular area:

The rectangular area is given as 75 meters by 50 meters. To find the area, we multiply the length by the width:

Area of rectangular area = Length * Width
= 75 meters * 50 meters
= 3750 square meters

Therefore, the total area of the rectangular area is 3750 square meters.

Step 2: Calculate the area of the crossroads:

Since the crossroads are parallel to the sides of the rectangle, they divide the rectangular area into four smaller rectangles. The dimensions of these smaller rectangles can be calculated by subtracting the width of the crossroads from the respective dimensions of the rectangular area.

The dimensions of the smaller rectangles are as follows:

- Top smaller rectangle: 75 meters by 2 meters
- Bottom smaller rectangle: 75 meters by 2 meters
- Left smaller rectangle: 50 meters by 2 meters
- Right smaller rectangle: 50 meters by 2 meters

To calculate the area of each smaller rectangle, we multiply the length by the width:

Area of each smaller rectangle = Length * Width

Calculating the area of each smaller rectangle:

- Top smaller rectangle: 75 meters * 2 meters = 150 square meters
- Bottom smaller rectangle: 75 meters * 2 meters = 150 square meters
- Left smaller rectangle: 50 meters * 2 meters = 100 square meters
- Right smaller rectangle: 50 meters * 2 meters = 100 square meters

Step 3: Calculate the area of the crossroads:

To find the area of the crossroads, we need to sum up the areas of the four smaller rectangles:

Area of crossroads = Sum of areas of the four smaller rectangles
= 150 square meters + 150 square meters + 100 square meters + 100 square meters
= 500 square meters

Therefore, the area of the crossroads is 500 square meters.

Step 4: Calculate the remaining area:

To find the remaining area within the rectangular area (excluding the crossroads), we subtract the area of the crossroads from the total area of the rectangular area:

Remaining area = Total area of rectangular area - Area of crossroads
= 3750 square meters - 500 square meters
= 3250 square meters

Therefore, the remaining area within the rectangular area is 3250 square meters.

Conclusion:

The area of the crossroads within the rectangular area is 500 square meters, while the remaining