The difference between the lengths of the parallel sides of a trapezium is 8 cm,

Let the length of the parallel sides be x and x − 8.
The height of the trapezium = 24 cm

Area of trapezium $=\frac{1}{2} \times$ sum of parallel sides $\times$ height

$\Rightarrow 312=\frac{1}{2} \times(x+x-8) \times 24$

⇒ 312 = 12(2x − 8)

$\Rightarrow 2 x-8=\frac{312}{12}$

⇒ 2x − 8 = 26
⇒ 2x = 26 + 8
⇒ 2x = 34
⇒ x = 17 cm

Hence, the lengths of the parallel sides are 17 cm and 9 cm.