Given:

Length of diagonal = 10√2 cm

Let the side of square = x cm

We know that,

Hypotenuse² = Base² + Perpendicular²

⇒ (10√2)² = x² + x²

⇒ 200 = 2x²

⇒ x² = 100

⇒ x = 10 cm

Now,

Area of a square = side²

= (10 cm)²

= 100 cm²