A rectangular lawn measuring 44 m by 32 m is to be surrounded externally by a path which is 4m wide. Find the area of the path.

Options

A. `248m^(2)`
B. `246m^(2)`
C. `1088m^(2)`
D. `672m^(2)`

Answer

To find the area of the path surrounding the rectangular lawn, we will follow these steps:

### Step 1: Calculate the dimensions of the outer rectangle (including the path).
- The original dimensions of the lawn are 44 m (length) and 32 m (width).
- The path is 4 m wide on all sides, so we need to add 4 m to each side of the rectangle.

**Calculation:**
- Length of the outer rectangle = 44 m + 4 m + 4 m = 52 m
- Width of the outer rectangle = 32 m + 4 m + 4 m = 40 m

### Step 2: Calculate the area of the outer rectangle.
- The area of a rectangle is given by the formula: Area = Length × Width.

**Calculation:**
- Area of the outer rectangle = 52 m × 40 m = 2080 m²

### Step 3: Calculate the area of the inner rectangle (the lawn).
- The area of the lawn is given by its original dimensions.

**Calculation:**
- Area of the inner rectangle = 44 m × 32 m = 1408 m²

### Step 4: Calculate the area of the path.
- The area of the path is the difference between the area of the outer rectangle and the area of the inner rectangle.

**Calculation:**
- Area of the path = Area of outer rectangle - Area of inner rectangle
- Area of the path = 2080 m² - 1408 m² = 672 m²

### Final Answer:
The area of the path is **672 m²**.

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