A 5m wide lawn is cultivated all along the outsides of a rectangular plot measuring ` 90 m xx 40 m `. The total area of the lawn is :

Options

A. `1441 m^(2) `
B. `1400 m^(2) `
C. `2600 m^(2) `
D. `420 m^2`

Answer

To find the total area of the lawn cultivated around the rectangular plot, we can follow these steps:

### Step-by-Step Solution

1. **Identify the dimensions of the rectangular plot:**
- Length = 90 m
- Width = 40 m

2. **Calculate the area of the rectangular plot:**
\[ \text{Area of the plot} = \text{Length} \times \text{Width} = 90 \, \text{m} \times 40 \, \text{m} = 3600 \, \text{m}^2 \]

3. **Determine the dimensions of the plot including the lawn:**
- The lawn is 5 m wide on all sides.
- New Length = Original Length + 5 m (on one side) + 5 m (on the other side)
\[ \text{New Length} = 90 \, \text{m} + 5 \, \text{m} + 5 \, \text{m} = 100 \, \text{m} \]
- New Width = Original Width + 5 m (on one side) + 5 m (on the other side)
\[ \text{New Width} = 40 \, \text{m} + 5 \, \text{m} + 5 \, \text{m} = 50 \, \text{m} \]

4. **Calculate the total area of the rectangular plot including the lawn:**
\[ \text{Total Area} = \text{New Length} \times \text{New Width} = 100 \, \text{m} \times 50 \, \text{m} = 5000 \, \text{m}^2 \]

5. **Find the area of the lawn:**
- The area of the lawn can be found by subtracting the area of the rectangular plot from the total area.
\[ \text{Area of the lawn} = \text{Total Area} - \text{Area of the plot} = 5000 \, \text{m}^2 - 3600 \, \text{m}^2 = 1400 \, \text{m}^2 \]

### Final Answer
The total area of the lawn is **1400 m²**.