Surface Area of Prisms – Ends Plus Lateral Faces
A prism's surface area splits neatly into two parts: the 2 end faces (identical copies of the cross-section) and the lateral surface area – the rectangular faces running along the length. The lateral surface area is always the cross-section's perimeter multiplied by the prism's length, since “unrolling” those rectangular sides gives one long rectangle with that width and length.
Putting it together: SA = 2 × (cross-section area) + (perimeter × length). This two-part approach – ends, then lateral surface – works for a prism with any cross-section shape, not just triangles.
Calculating a Prism's Surface Area
SA = 2 × (cross-section area) + (cross-section perimeter × length).
Triangle area = ½ × 6 × 8 = 24 cm². Perimeter = 6 + 8 + 10 = 24 cm. SA = 2 × 24 + (24 × 12) = 48 + 288 = 336 cm².
Real-Life Application
- Tents: calculating the fabric needed for a triangular-prism-shaped tent.
- Chocolate bar packaging: Toblerone-style triangular prism wrapping.
- Roof trusses: the surface area of a prism-shaped roof section.
Key Takeaways
- A prism's surface area is 2 end faces plus a lateral (rectangular) surface area.
- Lateral surface area = cross-section perimeter × prism length.
- This two-part method works for a prism with any cross-section shape.
Practice: Surface Area of Prisms
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