The area of a rhombus with side 13 cm and one diagonal 10 cm will be :

Side of a rhombus = 13 cm
Diagonal of rhombus = 10 cm
In ΔAOB
$$\eqalign{ & AO = \sqrt {{{13}^2} - {5^2}} \cr & \,\,\,\,\,\,\,\,\,\, = \sqrt {169 - 25} \cr & \,\,\,\,\,\,\,\,\,\, = \sqrt {144} \cr & \,\,\,\,\,\,\,\,\,\, = 12\,cm \cr} $$
$$\eqalign{ & \Rightarrow AC = 24 \cr & {\text{Area of rhombus :}} \cr & = \frac{1}{2} \times {d_1} \times {d_2} \cr & = \frac{1}{2} \times 24 \times 10 \cr & = 120\,sq.cm \cr} $$