The area of a rhombus having one side 10 cm and one diagonal 12 cm is

$\because$ Side of rhombus = 10 cm

In right angle triangle AOB

${\mathrm{AO}}^2={\mathrm{AB}}^2-{\mathrm{BO}}^2={10}^2-6^2=8^2$

$\therefore$ Other diagonal = AC

$\therefore AC=2\times AO=2\times 8=16 \mathrm{cm}$

$\therefore$ Area of rhombus $=\frac{1}{2}\times 12\times 16=96 {\mathrm{cm}}^2$.