A rectangular park is 100 m long and 60 m wide. There is a path 2 m wide out side the park. Find the area of the path?

Options

A. `324m^2`
B. `656 m^2`
C. `675 m^2`
D. `780 m^2`

Answer

To find the area of the path surrounding a rectangular park, we can follow these steps:

### Step 1: Calculate the area of the rectangular park.
The dimensions of the park are given as:
- Length = 100 m
- Width = 60 m

The area of the park can be calculated using the formula:
\[ \text{Area of the park} = \text{Length} \times \text{Width} \]
\[ \text{Area of the park} = 100 \, \text{m} \times 60 \, \text{m} = 6000 \, \text{m}^2 \]

### Step 2: Calculate the dimensions of the larger rectangle (park + path).
Since the path is 2 m wide on all sides, we need to add 2 m to both the length and the width of the park:
- New Length = \( 100 \, \text{m} + 2 \, \text{m} + 2 \, \text{m} = 104 \, \text{m} \)
- New Width = \( 60 \, \text{m} + 2 \, \text{m} + 2 \, \text{m} = 64 \, \text{m} \)

### Step 3: Calculate the area of the larger rectangle.
Using the new dimensions:
\[ \text{Area of the larger rectangle} = \text{New Length} \times \text{New Width} \]
\[ \text{Area of the larger rectangle} = 104 \, \text{m} \times 64 \, \text{m} \]

Calculating this:
\[ 104 \times 64 = 6656 \, \text{m}^2 \]

### Step 4: Calculate the area of the path.
The area of the path can be found by subtracting the area of the park from the area of the larger rectangle:
\[ \text{Area of the path} = \text{Area of the larger rectangle} - \text{Area of the park} \]
\[ \text{Area of the path} = 6656 \, \text{m}^2 - 6000 \, \text{m}^2 = 656 \, \text{m}^2 \]

### Final Answer:
The area of the path is \( 656 \, \text{m}^2 \).

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