The bases of a certain prism are equilateral triangles, and

since the area of the base is 9*sqrt(3) and the volume is 18*sqrt(3) we know that the height (h) of the prism is 2

the area of a triangle is base*height/2

since it is a equilateral triangle, we can choose any side to be the base (b), and the height (a) of the triangle can be calculated from the equation
(b/2)^2+a^2=b^2

which gives a=(sqrt(3)*b)/2

replacing "a" in the equation of the area of the triangle and making it equal to 9*sqrt(3) gives us:
9*sqrt(3)=b*b*sqrt(3)/(2*2)
which shows that b=6

b*h=12