A triangular prism has base area 6 cm², base perimeter 12 cm and length 10 cm.
- SA = 2B + Ph = 2(6) + 12(10).
- Total surface area is 132 cm².
Surface area of prisms & pyramids
Use the shape of every face.
Prisms have matching parallel bases
Calculate surface areas by adding the bases and lateral faces of prisms and pyramids.
For a right prism, SA = 2B + Ph, where B is the area of a base, P is its perimeter and h is the distance between bases. A net explains the lateral rectangles.
Explore the dimensions
Predict first, then change one dimension. Diagrams are schematic; results use the entered values. Rounded values are marked ≈.
Pyramids meet at an apex
A pyramid has one base and triangular lateral faces. Sum each triangle’s area and the base. In a regular pyramid, each triangle’s slant height is perpendicular to its base edge.
Slant height and vertical height differ
Slant height lies on a face and is used for that triangle’s area; the vertical height runs from the apex perpendicular to the base.
Worked examples
Square pyramid: base edge 4 cm, face slant height 5 cm.
- Base area = 16 cm²; each triangular face = 4×5÷2 = 10 cm².
- SA = 16 + 4(10) = 56 cm².
Guided Practice
A triangular prism has base area 12 cm², base perimeter 16 cm and length 5 cm. Find its surface area.
A first hint
Add two bases and the lateral rectangles.
Compare your reasoning
2(12) + 16(5) = 104 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
Explain why the lateral area of a right prism equals the perimeter of its base times its length.
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