A 5m wide lawn is cultivated all along the outside of rectangular plot measuring `80m xx 40m` The total area of the lawn is:

Options

A. `1200m^2`
B. `1300m^2`
C. `1350m^2`
D. `4800m^2`

Answer

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

### Step 1: Calculate the area of the rectangular plot.
The dimensions of the rectangular plot are given as:
- Length (L) = 80 m
- Breadth (B) = 40 m

The area of the rectangular plot can be calculated using the formula:
\[ \text{Area of the plot} = L \times B \]
\[ \text{Area of the plot} = 80 \, \text{m} \times 40 \, \text{m} = 3200 \, \text{m}^2 \]

### Step 2: Calculate the dimensions of the larger rectangle that includes the lawn.
Since the lawn is 5 m wide on all sides, we need to add twice the width of the lawn (5 m on each side) to both the length and the breadth of the plot.

New length (L') = Length of the plot + 2 × Width of the lawn
\[ L' = 80 \, \text{m} + 2 \times 5 \, \text{m} = 80 \, \text{m} + 10 \, \text{m} = 90 \, \text{m} \]

New breadth (B') = Breadth of the plot + 2 × Width of the lawn
\[ B' = 40 \, \text{m} + 2 \times 5 \, \text{m} = 40 \, \text{m} + 10 \, \text{m} = 50 \, \text{m} \]

### Step 3: Calculate the area of the larger rectangle that includes the lawn.
Now we can calculate the area of the larger rectangle:
\[ \text{Area of the rectangle with lawn} = L' \times B' \]
\[ \text{Area of the rectangle with lawn} = 90 \, \text{m} \times 50 \, \text{m} = 4500 \, \text{m}^2 \]

### Step 4: Calculate the area of the lawn.
To find the area of the lawn, we subtract the area of the rectangular plot from the area of the larger rectangle:
\[ \text{Area of the lawn} = \text{Area of the rectangle with lawn} - \text{Area of the plot} \]
\[ \text{Area of the lawn} = 4500 \, \text{m}^2 - 3200 \, \text{m}^2 = 1300 \, \text{m}^2 \]

### Final Answer:
The total area of the lawn is **1300 m²**.

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