To find the perimeter of a square when its diagonal is given, we can use the relationship between the diagonal $d$ and the side length $s$ of the square. For a square, the diagonal is related to the side by the following formula:

$d = s \sqrt{2}$

Given that the diagonal $d = 10\sqrt{2}$ cm, we can solve for $s$:

$s = \frac{d}{\sqrt{2}} = \frac{10\sqrt{2}}{\sqrt{2}} = 10 \, \text{cm}$

Now, to find the perimeter $P$ of the square, we use the formula:

$P = 4s = 4 \times 10 = 40 \, \text{cm}$

Thus, the perimeter of the square is 40 cm.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. What is the area of a square if its side length is 10 cm?
2. How do you calculate the side of a square if the area is known?
3. If the diagonal of a square is $12 \sqrt{2}$, what is its perimeter?
4. How does the length of the diagonal compare to the side length of a square?
5. What is the perimeter of a rectangle with sides 8 cm and 6 cm?

Tip: The diagonal of a square always forms a right triangle with two sides of the square, so you can use the Pythagorean theorem to connect the diagonal and side length.