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.

Correct 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=19.526 cma=5 \ \text{cm} \ \\ w=20 \ \text{cm} \ \\ \ \\ h_{2}=\sqrt{ 3 }/2 \cdot \ a=\sqrt{ 3 }/2 \cdot \ 5 \doteq 4.3301 \ \text{cm} \ \\ \ \\ w^2=h_{2}^2 + h^2 \ \\ \ \\ h=\sqrt{ w^2-h_{2}^2 }=\sqrt{ 20^2-4.3301^2 }=19.526 \ \text{cm}

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