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.

Result

h =  19.526 cm

Solution:

a=5 cm w=20 cm r=a=5=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≐19.5256=19.526  cm a = 5 \ cm \ \\ w = 20 \ cm \ \\ r = a = 5 = 5 \ cm \ \\ \ \\ s^2 = (a/2)^2 + w^2 \ \\ s = \sqrt{ (a/2)^2 + w^2 } = \sqrt{ (5/2)^2 + 20^2 } \doteq 20.1556 \ cm \ \\ \ \\ s^2 = r^2 + h^2 \ \\ \ \\ h = \sqrt{ s^2-r^2 } = \sqrt{ 20.1556^2-5^2 } \doteq 19.5256 = 19.526 \ \text{ cm }

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