**(c) 384 cm**^{2}.

Let AC = x. Then BD = \(\frac{3x}{4}\)

∴ OC^{2} + OB^{2} = BC^{2}

⇒ \(\frac{x^2}{4}\) + \(\frac{9x^2}{64}\) = 20^{2}

⇒ \(\frac{25x^2}{64}\) = 400 ⇒ x^{2 }= \(\frac{400\times64}{25}\) = 1024

⇒ x = 32 ⇒ AC = 32 cm and BD = 24 cm.

∴ Area of the rhombus = \(\frac12\) × AC × BD

= \(\frac12\) × 32 × 24 cm^{2} = **384 cm**^{2}.