## Key points

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.

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## How to calculate the surface area of a prism

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:

- Find the area of the two end faces.
- 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.

- Sum the areas of all the faces.

### Examples

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### Questions

Question 1: Find the total surface area of the prism.

Question 2: Find the total surface area of the triangular prism.

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## How to calculate the volume of a prism

The formula for the of a prism is:

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

To calculate the volume of a prism:

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

### Examples

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### Question

Find the volume of the prism.

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## Practise finding the surface area and volume of prisms

Practise finding the surface area and volume of prisms with this quiz. You may need a pen and paper to help you with your answers.

### Quiz

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## Real-life maths

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.

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### Game - Divided Islands

Divided Islands. gameDivided Islands

Use your maths skills to help the islanders of Ichi build bridges and bring light back to the islands in this free game from BBC Bitesize.

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