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Lateral Surface Area of a Pyramid

Result

1/4 n s sqrt(4 h^2 + s^2 cot^2(π/n))≈0.25 n s sqrt(4 h^2 + s^2 cot^2(3.14159/n))
(assuming n base vertices, base edge length s, and height h)

Visual representation


(drawn with base edge length 1, 5 base vertices, and height 2)

Properties of n-pyramid

slant height | sqrt(h^2 + 1/4 s^2 cot^2(π/n))≈sqrt(h^2 + 0.25 s^2 cot^2(3.14159/n))
volume | 1/12 h n s^2 cot(π/n)≈0.0833333 h n s^2 cot(3.14159/n)
lateral surface area | 1/4 n s sqrt(4 h^2 + s^2 cot^2(π/n))≈0.25 n s sqrt(4 h^2 + s^2 cot^2(3.14159/n))
base area | 1/4 n s^2 cot(π/n)≈0.25 n s^2 cot(3.14159/n)
surface area | 1/4 n s (sqrt(4 h^2 + s^2 cot^2(π/n)) + s cot(π/n))≈0.25 n s (sqrt(4 h^2 + s^2 cot^2(3.14159/n)) + s cot(3.14159/n))
(assuming n base vertices, base edge length s, and height h)

Back to List | POWERED BY THE WOLFRAM LANGUAGE