A rectangular park is 45m long and 30 m wide. A path of 2.5 mwide is constructed outside the park.

Break Down the Problem

1. Calculate the dimensions of the entire park including the path.
2. Determine the area of the park.
3. Calculate the area of the park plus the path.
4. Find the area of the path alone.

Relevant Concepts

• The area $A$ of a rectangle is calculated using the formula: $A = \text{length} \times \text{width}$
• When a uniform path surrounds a rectangular area, the new dimensions can be found by adding twice the width of the path (once for each side).

Analysis and Detail

1. Dimensions including the path:

   • Length including the path: $45 \, \text{m} + 2.5 \, \text{m} \times 2 = 45 + 5 = 50 \, \text{m}$
   • Width including the path: $30 \, \text{m} + 2.5 \, \text{m} \times 2 = 30 + 5 = 35 \, \text{m}$

2. Area of the park: $A_{\text{park}} = 45 \, \text{m} \times 30 \, \text{m} = 1350 \, \text{m}^2$

3. Area of the park plus the path: $A_{\text{total}} = 50 \, \text{m} \times 35 \, \text{m} = 1750 \, \text{m}^2$

4. Area of the path alone: $A_{\text{path}} = A_{\text{total}} - A_{\text{park}} = 1750 \, \text{m}^2 - 1350 \, \text{m}^2 = 400 \, \text{m}^2$

Verify and Summarize

• The dimensions were correctly calculated, and the areas have been computed step-by-step to ensure accuracy.

Final Answer

The area of the path alone is $400 \, \text{m}^2$.