To find the area of a square, we can first determine the side length from the perimeter and then use that to calculate the area.

1. Step 1: Use the formula for the perimeter of a square: $P = 4s$ where $P$ is the perimeter and $s$ is the side length of the square.

   Given that $P = 6.4$ meters, we can solve for $s$: $s = \frac{P}{4} = \frac{6.4}{4} = 1.6 \text{ meters}$

2. Step 2: Now, to find the area $A$ of the square, use the formula: $A = s^2$ Substituting the value of $s = 1.6$ meters: $A = (1.6)^2 = 2.56 \text{ square meters}$

Therefore, the area of the square is 2.56 square meters.

Would you like more details on any step, or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the area change if the perimeter of the square was doubled?
2. If the side length of the square is 2 meters, what is its perimeter?
3. How does the perimeter of a rectangle compare with a square if they both have the same area?
4. What is the length of the diagonal of this square?
5. How does the area of a square relate to its side length in general?

Tip: For any square, the side length can be easily found by dividing the perimeter by 4!