Wall height

Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.

Result

h =  19.526 cm

Solution:

a=5 cm n=6 w=20 cm  w1=a2−(a/2)2=52−(5/2)2≐4.3301 cm  h=w2−w12=202−4.33012≐19.5256≐19.526 cma=5 \ \text{cm} \ \\ n=6 \ \\ w=20 \ \text{cm} \ \\ \ \\ w_{1}=\sqrt{ a^2 - (a/2)^2 }=\sqrt{ 5^2 - (5/2)^2 } \doteq 4.3301 \ \text{cm} \ \\ \ \\ h=\sqrt{ w^2 - w_{1}^2 }=\sqrt{ 20^2 - 4.3301^2 } \doteq 19.5256 \doteq 19.526 \ \text{cm}

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