To find the length of the diagonal of a square when its area is given, we can follow these steps:

1. Area of a square: The area $A$ of a square is related to the side length $s$ by the formula: $A = s^2$ Given that the area is 228 $\text{u}^2$, we can solve for $s$: $s^2 = 228 \quad \Rightarrow \quad s = \sqrt{228}$ So, $s \approx 15.1$ units.

2. Diagonal of a square: The diagonal $d$ of a square is related to the side length by the Pythagorean theorem. Since the diagonal forms a right triangle with the sides of the square, the diagonal is given by: $d = s\sqrt{2}$ Substituting $s \approx 15.1$: $d \approx 15.1 \times \sqrt{2} \approx 15.1 \times 1.414 \approx 21.3 \, \text{units}$

Thus, the approximate length of the diagonal of the square is 21.3 units.

Would you like a more detailed explanation or further steps on related topics? Here are some questions you might find interesting:

1. How do you derive the formula for the diagonal of a square using the Pythagorean theorem?
2. What happens to the diagonal if the area of the square increases by a factor of 4?
3. Can the formula for the diagonal of a square be applied to other quadrilaterals?
4. What is the relationship between the perimeter and the diagonal of a square?
5. How do you calculate the area and diagonal of a rectangle?

Tip: The diagonal of a square is always longer than its side by a factor of $\sqrt{2}$, which is approximately 1.414.