we know that
[volume of a square prism]=b²*h
h=b/2
V=13.5 units³
then
13.5=b²*b/2------> b³=2*13.5------> b³=27--------> b=∛27------> b=3 units
h=b/2------> h=3/2-----> h=1.5 units
the answer is
the dimensions of the prism are
length of the square base is 3 units
height is 1.5 units