A rectangular grassy plot 160 m by 45 m has a gravel path 3 m wide all the four sides inside it . Find the area of the path

Options

A. 1194 sq m
B. 1226 sq m
C. 1294 sq m
D. 1312 sq m

Answer

To find the area of the gravel path surrounding the grassy plot, we will follow these steps:

### Step 1: Calculate the area of the grassy plot.
The dimensions of the grassy plot are given as:
- Length (L) = 160 m
- Breadth (B) = 45 m

The area of the grassy plot can be calculated using the formula:
\[ \text{Area of grassy plot} = L \times B \]

Substituting the values:
\[ \text{Area of grassy plot} = 160 \, \text{m} \times 45 \, \text{m} = 7200 \, \text{m}^2 \]

### Step 2: Calculate the dimensions of the inner rectangle (grassy area without the path).
Since the gravel path is 3 m wide on all four sides, we need to subtract 6 m from both the length and the breadth of the grassy plot (3 m on each side).

New dimensions:
- New Length = \( 160 \, \text{m} - 6 \, \text{m} = 154 \, \text{m} \)
- New Breadth = \( 45 \, \text{m} - 6 \, \text{m} = 39 \, \text{m} \)

### Step 3: Calculate the area of the inner rectangle (grassy area without the path).
Now, we calculate the area of the inner rectangle:
\[ \text{Area of inner rectangle} = \text{New Length} \times \text{New Breadth} \]

Substituting the new dimensions:
\[ \text{Area of inner rectangle} = 154 \, \text{m} \times 39 \, \text{m} = 6006 \, \text{m}^2 \]

### Step 4: Calculate the area of the gravel path.
The area of the gravel path can be found by subtracting the area of the inner rectangle from the area of the grassy plot:
\[ \text{Area of path} = \text{Area of grassy plot} - \text{Area of inner rectangle} \]

Substituting the values:
\[ \text{Area of path} = 7200 \, \text{m}^2 - 6006 \, \text{m}^2 = 1194 \, \text{m}^2 \]

### Final Answer:
The area of the gravel path is \( 1194 \, \text{m}^2 \).

---