The perimeter of a rhombus is 52 cm and one diagonal is 10 cm long. Then the area of the rhombus is

$4a=52\Rightarrow a=13{\text{cm}}^{\text{2}}$

$d_1=10\text{cm}$

In $\Delta ABO,A{B}^2=A{O}^2+B{O}^2\Rightarrow BO=12\text{cm}$

$\therefore d_2=2\left(12\right)=24\text{cm}$

$\therefore$  Area of Rhombus $\text{=}\frac{1}{2}{d}_1.d_2$

$=\frac{1}{2}\mathrm{.10.24}$

$=120{\text{cm}}^{\text{2}}$