A rectangular field is 30 m in length and 22 m in width. Two mutually perpendicular roads, each 2.5 m wide, are drawn inside the field so that one road is parallel to the length of the field and the other road is parallel to its width. Calculate the area of the crossroads.

Answer

To solve the problem of finding the area of the crossroads formed by two mutually perpendicular roads inside a rectangular field, we will follow these steps:

### Step 1: Understand the dimensions of the field and roads
The dimensions of the rectangular field are:
- Length = 30 m
- Width = 22 m

The width of each road is:
- Width of road = 2.5 m

### Step 2: Calculate the area of the first road (R1)
The first road (R1) is parallel to the length of the field. The area of R1 can be calculated using the formula for the area of a rectangle:
\[ \text{Area of R1} = \text{Length} \times \text{Width of road} \]
Substituting the values:
\[ \text{Area of R1} = 30 \, \text{m} \times 2.5 \, \text{m} = 75 \, \text{m}^2 \]

### Step 3: Calculate the area of the second road (R2)
The second road (R2) is parallel to the width of the field. The area of R2 is calculated similarly:
\[ \text{Area of R2} = \text{Width} \times \text{Width of road} \]
Substituting the values:
\[ \text{Area of R2} = 22 \, \text{m} \times 2.5 \, \text{m} = 55 \, \text{m}^2 \]

### Step 4: Calculate the area of the overlapping square
The two roads overlap in the area of a square where they intersect. The area of this square can be calculated as:
\[ \text{Area of square} = \text{Width of road} \times \text{Width of road} \]
Substituting the values:
\[ \text{Area of square} = 2.5 \, \text{m} \times 2.5 \, \text{m} = 6.25 \, \text{m}^2 \]

### Step 5: Calculate the total area of the crossroads
To find the total area of the crossroads, we add the areas of the two roads and subtract the area of the overlapping square:
\[ \text{Area of crossroads} = \text{Area of R1} + \text{Area of R2} - \text{Area of square} \]
Substituting the calculated values:
\[ \text{Area of crossroads} = 75 \, \text{m}^2 + 55 \, \text{m}^2 - 6.25 \, \text{m}^2 \]
\[ \text{Area of crossroads} = 130 \, \text{m}^2 - 6.25 \, \text{m}^2 = 123.75 \, \text{m}^2 \]

### Final Answer
The area of the crossroads is:
\[ \text{Area of crossroads} = 123.75 \, \text{m}^2 \]

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