A path of uniform width 4 m runs around the outside of a rectangular field 24 m by 18m. Find the area of the path.

Answer

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

### Step 1: Understand the dimensions of the field and the path
The rectangular field has a length of 24 meters and a breadth of 18 meters. The path surrounding the field has a uniform width of 4 meters.

### Step 2: Calculate the dimensions of the outer rectangle
Since the path is 4 meters wide on all sides, we need to add twice the width of the path (4 meters on each side) to both the length and the breadth of the field.

- **Outer Length** = Inner Length + 2 × Width of the Path
\[ \text{Outer Length} = 24 + 2 \times 4 = 24 + 8 = 32 \text{ meters} \]

- **Outer Breadth** = Inner Breadth + 2 × Width of the Path
\[ \text{Outer Breadth} = 18 + 2 \times 4 = 18 + 8 = 26 \text{ meters} \]

### Step 3: Calculate the area of the outer rectangle
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
So, the area of the outer rectangle is:
\[ \text{Area of Outer Rectangle} = 32 \times 26 = 832 \text{ square meters} \]

### Step 4: Calculate the area of the inner rectangle
Using the same formula for the area of the inner rectangle:
\[ \text{Area of Inner Rectangle} = 24 \times 18 = 432 \text{ square meters} \]

### Step 5: Calculate the area of the path
To find the area of the path, we subtract the area of the inner rectangle from the area of the outer rectangle:
\[ \text{Area of Path} = \text{Area of Outer Rectangle} - \text{Area of Inner Rectangle} \]
\[ \text{Area of Path} = 832 - 432 = 400 \text{ square meters} \]

### Final Answer
The area of the path is **400 square meters**.

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