A path 6 m wide runs around and outside of a rectangular plot of length 10 m and breadth 8 m. The area (in `m^2`) of the path is:

Options

A. 440
B. 600
C. 80
D. 360

Answer

To find the area of the path that runs around and outside a rectangular plot, we can follow these steps:

### Step 1: Find the dimensions of the inner rectangle
The inner rectangle represents the plot itself. Given:
- Length of the plot = 10 m
- Breadth of the plot = 8 m

### Step 2: Calculate the area of the inner rectangle
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Substituting the values:
\[ \text{Area of inner rectangle} = 10 \, \text{m} \times 8 \, \text{m} = 80 \, \text{m}^2 \]

### Step 3: Determine the dimensions of the outer rectangle
The path is 6 m wide and runs around the inner rectangle. Therefore, we need to add the width of the path to each dimension of the rectangle:
- New length = Length of the plot + 2 × Width of the path
\[ \text{New Length} = 10 \, \text{m} + 2 \times 6 \, \text{m} = 10 \, \text{m} + 12 \, \text{m} = 22 \, \text{m} \]
- New breadth = Breadth of the plot + 2 × Width of the path
\[ \text{New Breadth} = 8 \, \text{m} + 2 \times 6 \, \text{m} = 8 \, \text{m} + 12 \, \text{m} = 20 \, \text{m} \]

### Step 4: Calculate the area of the outer rectangle
Using the dimensions of the outer rectangle:
\[ \text{Area of outer rectangle} = \text{New Length} \times \text{New Breadth} \]
Substituting the values:
\[ \text{Area of outer rectangle} = 22 \, \text{m} \times 20 \, \text{m} = 440 \, \text{m}^2 \]

### Step 5: Calculate the area of the path
The area of the path is the difference between the area of the outer rectangle and the area of the inner rectangle:
\[ \text{Area of path} = \text{Area of outer rectangle} - \text{Area of inner rectangle} \]
Substituting the values:
\[ \text{Area of path} = 440 \, \text{m}^2 - 80 \, \text{m}^2 = 360 \, \text{m}^2 \]

### Final Answer
The area of the path is **360 m²**.