To find the area of a square garden given its perimeter, follow these steps:

Step 1: Use the formula for the perimeter of a square.

The formula for the perimeter $P$ of a square is: $P = 4 \times \text{side}$ We are given that the perimeter is 24 km, so: $24 = 4 \times \text{side}$

Step 2: Solve for the side length.

To find the side length, divide both sides of the equation by 4: $\text{side} = \frac{24}{4} = 6 \, \text{km}$

Step 3: Use the formula for the area of a square.

The formula for the area $A$ of a square is: $A = \text{side}^2$ Substitute the side length we found: $A = 6^2 = 36 \, \text{km}^2$

So, the area of the square garden is 36 square kilometers.

Do you need more details or have any questions?

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1. What is the relationship between the perimeter and area of a square?
2. How would the area change if the perimeter was doubled?
3. Can you derive the formula for the side of a square from the perimeter formula?
4. What are the units of area for a square with side lengths measured in kilometers?
5. How does the formula for a square's area compare with that of a rectangle?

Tip: The area of a square always grows faster than its perimeter because area depends on the square of the side length.