Closed box: 5 cm × 4 cm × 3 cm.
- Two base faces: 2(5 × 4) = 40 cm².
- Side pairs: 2(5 × 3) + 2(4 × 3) = 54 cm².
- Total surface area = 94 cm².
Surface area of rectangular prisms
Organize a net into pairs of faces.
Count every exposed face
Calculate closed and open rectangular-prism surface area and explain which faces are included.
For a closed rectangular prism, SA = 2lw + 2lh + 2wh. Each term represents a pair of congruent faces.
Explore the dimensions
Predict first, then change one dimension. Diagrams are schematic; results use the entered values. Rounded values are marked ≈.
Open containers need fewer faces
For a box with no top, SA = lw + 2lh + 2wh. State which face is missing rather than automatically using the closed-box formula.
A net supports the formula
Label each face and its dimensions. Add the areas once; convert all dimensions to a common unit first.
Worked examples
Remove the 5 cm × 4 cm lid.
- Subtract 20 cm² from the closed surface area.
- The open box needs 74 cm² of material, before tabs or overlap.
Guided Practice
An open box is 6 cm long, 4 cm wide and 2 cm high. Find its surface area.
A first hint
Count the bottom once and each pair of walls.
Compare your reasoning
6×4 + 2(6×2) + 2(4×2) = 64 cm².
Practice
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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Connections
Why can two boxes have the same volume but different surface areas?
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