Let's analyze and solve the question from the uploaded image.

Question Summary:

A square ground has a 2-meter-wide path all around it. The total area of the path is 1225 square meters. We need to determine the area of the ground alone.

Steps to Solve:

1. Denote Variables:

   • Let the side of the square ground be $x$ meters.
   • The ground, along with the path, forms a larger square. The side of the larger square becomes $x + 4$ meters (since the path is 2 meters wide on all sides).

2. Areas:

   • The total area of the larger square (ground + path) is: $(x + 4)^2$
   • The area of the ground alone is: $x^2$
   • The area of the path is the difference between the total area and the ground area: $\text{Area of path} = (x + 4)^2 - x^2$

3. Given Condition: $(x + 4)^2 - x^2 = 1225$

4. Expand and Simplify: Expand $(x + 4)^2$: $(x + 4)^2 = x^2 + 8x + 16$ Substitute into the equation: $x^2 + 8x + 16 - x^2 = 1225$ Simplify: $8x + 16 = 1225$ Solve for $x$: $8x = 1225 - 16 = 1209$ $x = \frac{1209}{8} = 151.125 \, \text{meters}$

5. Find the Ground Area: The area of the ground is: $x^2 = (151.125)^2 = 22838.7656 \, \text{square meters}.$

Final Answer:

The area of the ground alone is approximately: $\boxed{22838.77 \, \text{square meters}}$

Would you like further details on any part of the solution?

Related Questions:

1. How is the formula for the area of a square derived?
2. What are practical applications of calculating areas in real life?
3. How would the solution change if the path width was unequal on different sides?
4. What is the perimeter of the original square ground in this case?
5. Can you determine the total area of the larger square including the path?

Tip:

When dealing with geometric problems, always visualize the shape to understand how dimensions interact. This helps avoid calculation errors.