Surface Area of Pyramids
A pyramid has one base and triangular lateral faces. The key measurement is the slant height ().
Introduction
h = pyramid height, ℓ = slant height
Past Knowledge
Triangle area (11.1.1). Prism SA (12.2.1). Pythagorean theorem.
Today's Goal
Compute SA using SA = B + ½Pℓ.
Future Success
Cone SA (12.2.3), volume of pyramids (12.3.2).
Key Concepts
Regular Pyramid SA
B = base area, P = base perimeter, ℓ = slant height.
Slant Height vs. Pyramid Height
= slant height (along a face). = pyramid height (center to apex). Related by: where = apothem of the base.
Worked Examples
Square Pyramid
Base side = 8, slant height = 10.
B = 8² = 64. P = 4(8) = 32. LA = ½(32)(10) = 160.
SA = 224 sq units
Find Slant Height First
Square base s = 6, pyramid height h = 4. Find SA.
Base apothem = 6/2 = 3.
SA = 96 sq units
Common Pitfalls
Slant Height ≠ Pyramid Height
ℓ runs along the face, h is vertical. SA uses ℓ. Volume uses h. Don't mix them up.
Real-Life Applications
Egyptian Pyramids
The surface area of the Great Pyramid (originally covered in limestone) ~ 5.5 acres per face. SA formula was used to estimate the stone needed.
Practice Quiz
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