Hexagonal pyramid

Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.

Correct result:

h =  19.526 cm

Solution:

a=5 cm w=20 cm r=a=5 cm  s2=(a/2)2+w2 s=(a/2)2+w2=(5/2)2+202≐20.1556 cm  s2=r2+h2  h=s2−r2=20.15562−52=19.526 cma=5 \ \text{cm} \ \\ w=20 \ \text{cm} \ \\ r=a=5 \ \text{cm} \ \\ \ \\ s^2=(a/2)^2 + w^2 \ \\ s=\sqrt{ (a/2)^2 + w^2 }=\sqrt{ (5/2)^2 + 20^2 } \doteq 20.1556 \ \text{cm} \ \\ \ \\ s^2=r^2 + h^2 \ \\ \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 20.1556^2-5^2 }=19.526 \ \text{cm}

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