parallelepiped

The trick here is to know something about the properties of a rhombus.

The area of a rhombus is the product of the diagonals. So if I call one diagonal p and the other q, then
p*q=1m^2

Think now about the diagonal crosss sections. They will be parallelograms with a height the height of the parallelepiped and a base equal to p ,in one case, and q in the other.
so
p*h=3m^2
and
q*h=6m^2
taking the product of the latter two equations you get
(p*h)(q*h)=3m^2*6m^2=18m^4
so
(p*q)h^2=18m^4
now remember
p*q=1m^2
substituting
(1m^2)h^2=18m^4
h^2=18m^2
so
h=sqrt(18)m

Now you know the base and the height of the parallelepiped. The volume is the product [1m^2*3sqrt(2)m=3sqrt(2)m^3]

Rap

Thanks, but the answer should be 3m^3 not 3sqrt(2)m^3.Why??