🔥 How to Find Surface Area
The Big Idea: Unfold the Prism
1
Look at the
net (unfolded shape). Each colored face shows one surface.
Each face is labeled with its two dimensions.
2
Find the area of each face by multiplying its two dimensions (length × width).
3
Add all face areas together. That total is the surface area.
▭ Rectangular Prism — 6 faces, 3 matching pairs
Top & Bottom: l × w
Left & Right: w × h
Front & Back: l × h
SA = 2(l×w) + 2(w×h) + 2(l×h)
Example: l=3, w=4, h=5 → 2(12)+2(20)+2(15) = 24+40+30 = 94 sq units
△ Triangular Prism — 5 faces
2 Triangles: ½×base×height
Rect 1: leg₁ × L
Rect 2: leg₂ × L
Rect 3: hyp × L
For a right-triangle base: SA = leg₁×leg₂ + (leg₁+leg₂+hyp)×L
Example: legs 3&4, hyp 5, L=6 → 3×4 + (3+4+5)×6 = 12+72 = 84 sq units
