The lengths of the parallel sides of a trapezium are x cm and y cm and the area of the trapezium is $\frac{1}{2}$(x² - y²) cm². What is the distance between the parallel sides (in cm) ?

x - y

The area of the trapezium = $\frac{1}{2}$(x² - y²)

If the lengths of the parallel sides of a trapezium are x cm and y cm and its height is h cm then, the area of the trapezium = $\frac{1}{2}$(x + y)h

The area of the trapezium = $\frac{1}{2}$(x² - y²) = $\frac{1}{2}$(x - y)(x + y)

$\frac{1}{2}$(x + y)h = $\frac{1}{2}$(x - y)(x + y) 

On comparing both of these equations given above,

h = (x - y)