Regular hexagonal pyramid

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

Result

h =  19.526 cm

Solution:

a=5 cm w=20 cm  h2=3/2⋅ a=3/2⋅ 5≐4.3301 cm  w2=h22+h2  h=w2−h22=202−4.33012≐19.5256=19.526  cm a = 5 \ cm \ \\ w = 20 \ cm \ \\ \ \\ h_{ 2 } = \sqrt{ 3 }/2 \cdot \ a = \sqrt{ 3 }/2 \cdot \ 5 \doteq 4.3301 \ cm \ \\ \ \\ w^2 = h_{ 2 }^2 + h^2 \ \\ \ \\ h = \sqrt{ w^2-h_{ 2 }^2 } = \sqrt{ 20^2-4.3301^2 } \doteq 19.5256 = 19.526 \ \text{ cm }

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