A rectangular grassy lawn is 18 m by 12 m. It has a gravel path 1.5 m wide all around it on the outside. What is the area of the path .

Answer

To find the area of the gravel path surrounding the rectangular grassy lawn, we can follow these steps:

### Step 1: Determine the dimensions of the lawn
The dimensions of the rectangular lawn are given as:
- Length = 18 m
- Width = 12 m

### Step 2: Calculate the dimensions of the entire area including the path
Since the gravel path is 1.5 m wide around the lawn, we need to add twice the width of the path to both the length and the width of the lawn:
- New Length = Length of lawn + 2 * Width of path
\[ = 18 \, \text{m} + 2 \times 1.5 \, \text{m} = 18 \, \text{m} + 3 \, \text{m} = 21 \, \text{m} \]
- New Width = Width of lawn + 2 * Width of path
\[ = 12 \, \text{m} + 2 \times 1.5 \, \text{m} = 12 \, \text{m} + 3 \, \text{m} = 15 \, \text{m} \]

### Step 3: Calculate the area of the entire rectangle (lawn + path)
Now we can calculate the area of the larger rectangle that includes both the lawn and the path:
\[ \text{Area of larger rectangle} = \text{New Length} \times \text{New Width} = 21 \, \text{m} \times 15 \, \text{m} = 315 \, \text{m}^2 \]

### Step 4: Calculate the area of the lawn
Next, we calculate the area of the lawn itself:
\[ \text{Area of lawn} = \text{Length} \times \text{Width} = 18 \, \text{m} \times 12 \, \text{m} = 216 \, \text{m}^2 \]

### Step 5: Calculate the area of the path
Finally, we find the area of the path by subtracting the area of the lawn from the area of the larger rectangle:
\[ \text{Area of path} = \text{Area of larger rectangle} - \text{Area of lawn} = 315 \, \text{m}^2 - 216 \, \text{m}^2 = 99 \, \text{m}^2 \]

### Conclusion
The area of the gravel path is \( 99 \, \text{m}^2 \).

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