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 vertex count, base edge length s, and height h)

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

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 vertex count, base edge length s, and height h)