To solve the problem:

1. Determine the dimensions of the outer square:

   • The lawn has a side length of 8 meters.
   • The path around the lawn is 50 cm wide, which is $0.5 \, \text{m}$ (converted to meters).
   • The total width including the path on both sides is $8 + 2 \times 0.5 = 9 \, \text{m}$.
     Thus, the outer square has a side length of $9 \, \text{m}$.

2. Calculate the area of the outer square: $\text{Area of the outer square} = \text{side}^2 = 9^2 = 81 \, \text{m}^2$

3. Calculate the area of the lawn (inner square): $\text{Area of the lawn} = \text{side}^2 = 8^2 = 64 \, \text{m}^2$

4. Calculate the area of the path: The path is the area of the outer square minus the area of the lawn: $\text{Area of the path} = 81 - 64 = 17 \, \text{m}^2$

Final Answer:

The area of the path is 17 m².

Would you like further explanation or details?

Related Questions:

1. How is the area of a square calculated?
2. What is the importance of converting units (e.g., cm to meters) in such problems?
3. How would the area change if the width of the path were doubled?
4. How do you calculate the perimeter of the outer square?
5. What if the lawn were a rectangle instead of a square—how would the calculation change?

Tip:

Always convert all measurements to the same unit before performing calculations to ensure accuracy.