A trapezium is made up of a rectangle and a triangle. This can be written as:

(area)=(rectangle)+(triangle)

Let the 'h' represent the heights of both the rectangle and triangle (which are the same height), 'x' represent the the base of the rectangle (this is the same as the shorter of the parallel sides), and 'y' represent the base of the triangle (this is the same as the overlap of the two parallel sides). Therefore, we can write:

area=(hx)+(.5hy)

Now, we can plug in numbers for x, y, and h based on the given information. We get:

50=(4)(x)+.5(4)(5)

Solving for 'x' (the shorter parallel side), we get:

x=10cm

Therefore, the parallel sides are 10cm and 15cm in length.