**(a)** **96 cm**^{2}

Since the diagonals of a rhombus bisect each other at right angles.

In Δ AOB, BO^{2} = \(\sqrt{AB^2-AO^2}\)

= \(\sqrt{100-64}\) cm

= \(\sqrt{36}\) = 6 cm

∴ The other diagonal = 2 × 6 cm = 12 cm

∴ Area of the rhombus = \(\frac12\) × 16 cm × 12 cm = **96 cm**^{2}.