find the area of the cross section then multiply by the other dimension (length, height, whatever you are calling it)
Area of a parallelogram is base x height, area of a kite might need to be broken into triangles then added together.
length = volume/cross-section
Parallelogram
You need to know the area of that cross-section. Once you have that number, the volume of the box is the product of (cross-section area) x (height).
Volume in cubic feet = cross-section area*length
The volume of a bottle is not sufficient information to determine its dimensions. Some bottles have a wide circular cross section and are squat, others have a smaller cross section but are taller, others have a square or rectangular cross section.
Volume of a parallelogram = cross-section area times length
length = volume/cross-section
There is no difference in the sense that the volume for either is the length times the area of cross-section.
It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.
Volume = area of cross-section*length
The cross section volume of a trapezoid is found between 0 and 2.0.
To find the volume of a prism you first need to know the area of cross section. Then, Volume of prism = area of cross section x length.
Parallelogram
You need to know the area of that cross-section. Once you have that number, the volume of the box is the product of (cross-section area) x (height).
Volume = cross-section area*length
Volume = cross-section area*length
Multiply the cross-section area by the height.