The task presented in this image asks to calculate the length of a square's side (denoted as $x$) given the area of the square. The formula relating the area $A$ of a square to the side length $x$ is:

$A = x^2$

To find $x$, we simply take the square root of the given area:

$x = \sqrt{A}$

Let's solve for each case:

1. a) $A = 16 \, \text{m}^2$: $x = \sqrt{16} = 4 \, \text{m}$

2. b) $A = 64 \, \text{m}^2$: $x = \sqrt{64} = 8 \, \text{m}$

3. c) $A = 81 \, \text{m}^2$: $x = \sqrt{81} = 9 \, \text{m}$

4. d) $A = 100 \, \text{m}^2$: $x = \sqrt{100} = 10 \, \text{m}$

Summary:

• a) $x = 4 \, \text{m}$
• b) $x = 8 \, \text{m}$
• c) $x = 9 \, \text{m}$
• d) $x = 10 \, \text{m}$

Would you like further details on any of these steps? Here are five related questions:

1. What is the formula for the area of a square, and why does it involve squaring the side?
2. How do we find the square root of non-perfect squares?
3. What are some real-world applications of calculating the side length from the area of squares?
4. How does this method apply to other shapes like rectangles?
5. Can we solve for the side of a square when the area is given in different units (e.g., square kilometers)?

Tip: When working with geometric shapes, always check that the units of measurement are consistent, especially when calculating areas or lengths.