What would be the measure of the diagonal of a square whose area is equal to 578 sq cm?

Let’s denote the side length of the square as \(s\) cm.

The area of the square is given as 578 sq cm, so we can write:

\[ \text{Area} = s^2 = 578 \text{ sq cm} \]

To find the side length \(s\), we take the square root of the area:

\[ s = \sqrt{578} \text{ cm} \]

The diagonal of a square is given by \(d = s\sqrt{2}\), so the length of the diagonal is:

\[ d = \sqrt{578} \times \sqrt{2} = \sqrt{1156} \text{ cm} = 34 \text{ cm} \]

Therefore, the measure of the diagonal of the square is 34 cm.