f0;️ How to Find Surface Area
The Big Idea: Unfold the Pyramid
1
Look at the net. Each colored face is one surface of the pyramid.
2
Find the area of each face. The base is a rectangle or triangle. Every lateral face is a triangle: Area = ½ × base × slant height.
3
Add all face areas for the total surface area.
▱ Rectangular / Square Pyramid — 5 faces
Base: l × w
2 long faces: 2 × (½×l×sl)
2 short faces: 2 × (½×w×sl)
SA = l×w + l×sl₁ + w×sl₂
Square pyramid (l=w=s, one slant height): SA = s² + 2×s×sl
△ Triangular Pyramid — 4 triangular faces
Strip (all faces equal)
SA = 4 × (½ × a × h) = 2ah
Fan (base different from lateral)
SA = ½ahb + 3 × (½ × a × sl)
1 base face: ½ × a × h
3 lateral faces: 3 × (½ × a × h)
SA = 4 × (½ × a × h) = 2 × a × h
All 4 faces identical → multiply one face area by 4
