The area of a //-gram is

A=b*h, where

b=the length of the base,

h=the length of the height.

Now A is given 54 cm^2 & b=6 cm

=>

6h=54

=>

h=54/6

=>

h=9 cm.

h = 9 cm

height = 54/6 = 9 cm

Area of parallelogram = base x perpendicular height

Hence

54 = 6 cm x ph cm

perpendicular height = 9 cm

This is the right angles (90degree) height

The 'sloping' height will be of a different value.

A = b h

54 = 6 h

h= 54/6 = 9 cm

parallelogram

A = sh = pq/2

where h is the height, s is a side and p,q are the diagonals.

54 = 6h

h = 9 cm