A square lawn is surrounded by a path 2m wide. If the area of the path is 240m², find the area of the lawn?

To find the area of the square lawn, we first need to determine the dimensions of the lawn and the surrounding path.

Understanding the Problem

Let the side length of the square lawn be x meters. The path surrounding the lawn is 2 meters wide, which means the total side length including the path is x + 4 meters (2 meters on each side).

Calculating the Areas

• The area of the larger square (lawn + path) is: (x + 4)²
• The area of the lawn itself is: x²

Finding the Area of the Path

The area of the path can be calculated by subtracting the area of the lawn from the area of the larger square:

Area of the path = Area of larger square - Area of lawn

Given that the area of the path is 240 m², we can set up the equation:

(x + 4)² - x² = 240

Simplifying the Equation

Expanding the left side:

(x² + 8x + 16) - x² = 240

This simplifies to:

8x + 16 = 240

Solving for x

Now, we can solve for x:

• Subtract 16 from both sides: 8x = 224
• Divide by 8: x = 28

Calculating the Area of the Lawn

Now that we have the side length of the lawn, we can find its area:

Area of the lawn = x² = 28² = 784 m²

Final Answer

The area of the lawn is 784 m².

To find the area of the square lawn, we first need to understand the relationship between the lawn and the surrounding path.

Step 1: Determine the dimensions of the path and lawn

Let the side length of the square lawn be x meters. The path surrounding the lawn is 2 meters wide, which means the total side length of the lawn plus the path is x + 4 meters (2 meters on each side).

Step 2: Calculate the area of the larger square

The area of the larger square (lawn plus path) can be calculated as:

Area of larger square = (x + 4)²

Step 3: Calculate the area of the lawn

The area of the lawn itself is:

Area of lawn = x²

Step 4: Find the area of the path

The area of the path is the area of the larger square minus the area of the lawn:

Area of path = (x + 4)² - x²

According to the problem, the area of the path is 240 m². Therefore, we can set up the equation:

(x + 4)² - x² = 240

Step 5: Simplify the equation

Expanding the left side:

(x² + 8x + 16) - x² = 240

This simplifies to:

8x + 16 = 240

Step 6: Solve for x

Subtract 16 from both sides:

8x = 224

Now, divide by 8:

x = 28

Step 7: Calculate the area of the lawn

Now that we have the side length of the lawn, we can find its area:

Area of lawn = x² = 28² = 784 m²

Final Result

The area of the lawn is 784 m².