Prism nets and surface area
Unfold a solid, identify all faces and total the area of its outer surface.
Before you begin
- Rectangle and triangle areas
- Recognising prisms
Use a net to account for every face
A net is a flat arrangement of faces that can fold into a solid. A rectangular prism has six rectangular faces in three equal pairs. A triangular prism has two matching triangular ends and three rectangular side faces. Label shared edge lengths on the net before calculating. Faces may look different when rotated on the page but still have equal dimensions.
Match the surface to the context
Surface area is the sum of the areas of the included faces. A closed box includes all six faces, but a lidless container excludes its top. Wallpaper, paint and wrapping problems may also specify uncovered or overlapping areas. Surface area uses square units and is distinct from the volume inside. Explain which faces you included instead of relying on a memorised formula alone.
Worked example
Find the surface area of a closed box measuring 4 cm by 3 cm by 2 cm.
Show the worked solution
- The top and bottom each have area 4 × 3 = 12 cm², giving 24 cm².
- The other pairs give 2 × 4 × 2 = 16 cm² and 2 × 3 × 2 = 12 cm².
- Add all six faces: 24 + 16 + 12 = 52 cm².
52 cm².
Try it yourself
The same box has no lid. Which area should be removed from 52 cm²?
Common mistakes
- Count each outside face exactly once.
- Surface area is measured in square units, not cubic units.
What can you explain now?
A triangular prism has right-triangle ends with sides 3, 4 and 5 cm and a length of 6 cm. Find its total surface area.
Compare with the explanation
84 cm².
The two ends total 2 × (3 × 4/2) = 12 cm². The side rectangles total (3 + 4 + 5) × 6 = 72 cm². The sum is 84 cm².
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗