Volume of a prism

A prism is a solid shape that has the same cross-section all the way through.

Diagram set of three prism shapes.

These three shapes are prisms.

  • The first has a circular cross-section.
  • The second has a rectangular cross-section.
  • The third has a triangular cross-section.

(Sometimes the ‘cross-section’ is called the 'base'.)

The distance between the two ends of the prism is always called the height of the prism even if the prism is lying horizontally (like the triangular prism above).

Diagram set of two non-prism shapes.

These two shapes are not prisms.The cross-section changes at each level.

For any prism:

Volume = Area\, of\, cross-section\,\times height\, of\, prism

Diagram of an isoceles prism with the values 6cm wide, 4cm tall and 12cm deep.

This shape is a triangular prism so the area of the cross-section is the area of a triangle.

Area of the triangle:

= \frac{1}{2} \times 6 \times 4

= 12cm^{2}

Volume\,of\,prism\,= Area\,of\,cross-section\times height\,of\,prism

= 12 \times 13

= 156cm^{3}