Boxes and prisms

The volume of a solid is how much space it fills. For the whole family of box-shaped solids, one idea is behind all of it: stack the base.

Base area, times height

A box is a rectangle — the base — repeated all the way up to its height. So its volume is the area of the base × the height:

V = length × width × height

A box 3 × 2 × 2 units holds 3 × 2 × 2 = 12 cubic units.

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Why "prism" means the same thing

Any solid with the same cross-section all the way up — a triangular prism, an L-shaped slab, a hexagonal column — is a prism, and the rule never changes: area of the base, times the height. The base can be any shape; the stacking is what makes it a volume.