Given:

Length of diagonal 1 (d₁) = 24 cm

Side = 20 cm

Let, Length of diagonal 2 be d₂

We know that,

Side of rhombus = 1/2 × √(d₁² + d₂² )

⇒ 20 = 1/2 × √(24² + d₂² )

⇒ 20 × 2 = √(576 + d₂² )

⇒ 40 = √(576 + d₂²)

Squaring both sides,

⇒ 1600 = 576 + d₂²

⇒ d₂² = 1600-576

⇒ d₂² = 1024

⇒ d₂ = 32 cm

Now,

Area of rhombus= 1/2 × d₁ × d₂

= 1/2 × 24 × 32

= 384 cm²