Surface area and volume of prisms - KS3 Maths - BBC Bitesize (2024)

• A has a constant . The cross-section is a .

• The is made up of at either end of the prism and a set of rectangles between them. The number of rectangular faces is the same as the number of of the shape at each end of the prism.

• Understanding of shapes and the area of different shapes helps when working out the surface area of a prism. Surface area is measured in square units, such as cm² and mm².

• The of a prism is the area of its cross-section multiplied by the length. Volume is measured in cubed units, such as cm³ and mm³.

• A can be named by the shape of its .

  • When the cross-section is a triangle, the prism is called a triangular prism.
  • When the cross-section is a hexagon, the prism is called a hexagonal prism.

• A is not a prism. The cross-section of a prism is a polygon, a shape bounded by straight lines. A circle is not a polygon.

The surface area is made up of the end faces and rectangular faces that join them.

• To calculate the total surface area of a prism:

1. Find the area of the two end faces.
2. Work out the area of all the rectangular faces in one of two ways:
   • Work out the area of each rectangle separately, length × width.
   • Multiply the perimeter of the end face by the length of the prism.
3. Sum the areas of all the faces.

The formula for the of a prism is:

\(Volume =\) \(Area\) \(of\) \(cross\)-\(section\) × \(length\)

To calculate the volume of a prism:

1. Work out the area of the .
2. Multiply by the length (or height) of the prism.

Manufacturers often use prism-shaped containers for their products. Triangular prisms and hexagonal prisms are popular choices for packaging for chocolate or cakes, for example, or for gift boxes and glasses cases.

In order to create the prism-shaped boxes, the surface area is designed with a little extra added on. This allows for tabs that are glued or fixed to hold the box or container together when it is folded up, making the complete prism shape.