The area of a trapezium is 405 cm

Let the lengths of the parallel sides of the trapezium be $4 x \mathrm{~cm}$ and $5 x \mathrm{~cm}$, respectively.

Now,

Area of trapezium $=\left\{\frac{1}{2} \times(4 x+5 x) \times 18\right\} \mathrm{cm}^{2}$

$=\left(\frac{1}{2} \times 9 x \times 18\right) \mathrm{cm}^{2}$

$=81 x \mathrm{~cm}^{2}$

Area of trapezium $=405 \mathrm{~cm}^{2} \quad$ (Given)

$\therefore 81 x=405$

$\Rightarrow x=\frac{405}{81}$

$\Rightarrow x=5 \mathrm{~cm}$

Length of one side $=(4 \times 5) \mathrm{cm}=20 \mathrm{~cm}$

Length of the other side $=(5 \times 5) \mathrm{cm}=25 \mathrm{~cm}$