Given:

Length of diagonal = 24 cm

Let the side of square = x cm

We know that,

Hypotenuse² = Base² + Perpendicular²

⇒ 24² = x² + x²

⇒ 576 = 2x²

⇒ x² = 288

⇒ x = 12√2 cm

Now,

Area of a square = side²

= (12√2 cm)²

= 288 cm²