The area of a trapezium is 1080 cm

Let the distance between the parallel sides be $x$.

Now,

Area of trapezium $=\left\{\frac{1}{2} \times(55+35) \times x\right\} \mathrm{cm}^{2}$

$=\left(\frac{1}{2} \times 90 \times x\right) \mathrm{cm}^{2}$

$=45 x \mathrm{~cm}^{2}$

Area of the trapezium $=1080 \mathrm{~cm}^{2}$ (Given)

$\therefore 45 x=1080$

$\Rightarrow x=\frac{1080}{45}$

$\Rightarrow x=24 \mathrm{~cm}$

Hence, the distance between the parallel sides is $24 \mathrm{~cm} .$