Prisms (Edexcel GCSE Maths): Revision Notes
Prisms
What is a prism?
A prism is a three-dimensional shape that has the same cross-section throughout its entire length. Think of it like a tube where if you slice it anywhere along its length, you'll always get the same shape. The cross-section could be a triangle, rectangle, trapezium, or any other 2D shape.
The key characteristic of a prism is its constant cross-section. This property is what makes the volume formula so straightforward to apply.
Volume of prisms
The formula
To find the volume of any prism, you use this key formula:
This works because you're essentially stacking identical cross-sections along the length of the prism.
Method for calculating volume
- Identify the cross-section - this is usually shown as the shaded end of the prism
- Calculate the area of the cross-section using the appropriate area formula
- Multiply by the length of the prism
The cross-section is typically the shaded or highlighted face in diagrams. Always look for visual cues that indicate which face represents the cross-section.
Worked example: Trapezium prism
Worked Example: Trapezium Prism Volume
Consider a prism with a trapezoidal cross-section where:
- Parallel sides are 6cm and 10cm
- Height is 5cm
- Length of prism is 7cm
Step 1: Find the area of the trapezium cross-section
- Area of trapezium =
- Area =
Step 2: Calculate the volume
- Volume = Area of cross-section × Length
- Volume =
Surface area of prisms
The method
To find the surface area of a prism, you need to add together the areas of all faces. This includes:
- The two identical end faces (cross-sections)
- All the rectangular faces that connect the ends
Important tip: Remember to include faces you cannot see in the diagram - sketch each face separately with its dimensions to avoid missing any.
Worked example: Triangular prism
Worked Example: Triangular Prism Surface Area
For a triangular prism, you would calculate:
- Area of both triangular end faces
- Area of each rectangular side face
- Add all these areas together
The total surface area is the sum of all individual face areas.
Problem solving with prisms
Sometimes you'll be given the volume of a prism and asked to find a missing dimension. In these cases, you can use the reverse process:
General Problem-Solving Method:
- Set up the volume equation using the known information
- Substitute the known values into Volume = Area of cross-section × Length
- Solve the resulting equation to find the unknown dimension
Example approach
If a cube and triangular prism have the same volume, and you know most dimensions, you can:
- Calculate the cube's volume using
- Set this equal to the prism's volume formula
- Solve for the missing dimension
Key formulas to remember
The essential formulas for prism calculations:
- Volume of prism =
- Area of triangle =
- Area of trapezium =
- Surface area = Sum of all face areas
Common Mistakes to Avoid:
- Forgetting to include hidden faces when calculating surface area
- Mixing up units (using cm instead of cm² or cm³)
- Not identifying the correct cross-section in complex diagrams
Exam tips
Essential Exam Strategies:
- Show all your working - you can gain marks for correct method even if your final answer is wrong
- Write down what you're calculating at each stage to make your working clear
- Check your units - volumes are in cubic units (cm³, m³) and areas are in square units (cm², m²)
- Draw and label each face separately when calculating surface area to avoid missing any
Key Points to Remember:
- A prism has a constant cross-section throughout its length
- Volume = Area of cross-section × Length works for all prisms
- Surface area requires you to find and add all face areas (including hidden ones)
- Always show your working in exams - partial marks are available for correct methods
- Double-check units - volume uses cubic units, area uses square units