Step 1 of 10
Start
Surface area measures every outside face.
Demo prism
triangle sides 3, 4, 5 cm · prism length 10 cm
triangle sides 5, 12, 13 cm · prism length 8 cm
Count
faces
faces
›
Unfold
net
net
›
Find face
areas
areas
›
Add
outside
outside
Packaging model
A prism has an outside skin
Surface area is wrapping material: no inside space, and no face left out.
2 × triangle
3 × rectangle
Unzip the wrapper into a net
Fold lines keep each face attached while the prism opens flat.
2 triangle ends
3 side rectangles
Calculate the two triangle ends
× 2 matching ends
Triangle faces
2 × (½ × 3 × 4) = 12 cm²
Calculate the rectangle strip
× prism length
Rectangle faces
(3 + 4 + 5) × 10 = 120 cm²
Add the whole outside
Two kinds of faces. One complete surface.
2 triangles2(½ × 3 × 4) = 12
3 rectangles(3 + 4 + 5) × 10 = 120
Surface area12 + 120 = 132 cm²
+ add every face
SA = 2B + P × L
B = one triangle’s area · P = triangle perimeter · L = prism length
Your turn: account for every face
Triangle sides 5, 12, 13 cm. Prism length 8 cm.
Enter each subtotal, then the total.
Use the net: triangle pair + rectangle strip.
Solve on your whiteboard
Show the two triangle faces, the three rectangles, and the final sum. Submit your work when you are ready.
Work submitted. The net is ready to reveal.
Build the same two-part total
1 triangle½ × 5 × 12 = 30
2 triangles2 × 30 = 60
Perimeter5 + 12 + 13 = 30
3 rectangles30 × 8 = 240
Surface area60 + 240 = 300 cm²
+ join both parts of the net
SA = 2B + P × L = 300 cm²
Every face accounted for.
For any triangular prism, find both triangle ends, find the three side rectangles, then add. Surface area always uses square units.
2 + 3five faces
2B + PLtwo parts
cm²square units