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

(drawn with base edge length 1, 11 base vertex count, and height 2)

volume | 1/4 h n s^2 cot(π/n)≈0.25 h n s^2 cot(3.14159/n) lateral surface area | h n s base area | 1/4 n s^2 cot(π/n)≈0.25 n s^2 cot(3.14159/n) surface area | n s (h + 1/2 s cot(π/n))≈n s (h + 0.5 s cot(3.14159/n)) (assuming n base vertex count, base edge length s, and height h)