A prism has two congruent parallel polygonal end faces and a uniform cross-section between them. Its volume is V=AL, where A is the cross-sectional area and L is the perpendicular separation of the end faces. Think of stacking equal thin layers. **Solid** | **Volume** Cuboid of length l, width w, height h | lwh Cube of side s | s3 Prism of cross-sectional area A and perpendicular length L | AL Example A triangular prism has a right-triangle cross-section with perpendicular sides 3 cm and 4 cm, and length 10 cm. Its cross-sectional area is 12 x 3 x 4=6 cm2, so its volume is 60 cm3. For an oblique prism, the sloping joining edge is not the perpendicular separation of the bases. The volume formula uses that perpendicular separation.

A prism has two congruent parallel polygonal end faces and a uniform cross-section between them. Its volume is \(V=AL\), where \(A\) is the cross-sectional area and \(L\) is the perpendicular separation of the end faces. Think of stacking equal thin layers.

A triangular prism has a right-triangle cross-section with perpendicular sides 3 cm and 4 cm, and length 10 cm. Its cross-sectional area is \(\dfrac12\times3\times4=6\text{ cm}^2\), so its volume is \(60\text{ cm}^3\).

For an oblique prism, the sloping joining edge is not the perpendicular separation of the bases. The volume formula uses that perpendicular separation.

Solid	Volume
Cuboid of length l, width w, height h	\(lwh\)
Cube of side s	\(s^3\)
Prism of cross-sectional area A and perpendicular length L	\(AL\)

Volume from a uniform cross-section

Volume from a uniform cross-section