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 answer:

h =  19.5256 cm

Step-by-step explanation:

$$\begin{gathered} a=5\text{ cm } \\ w=20\text{ cm } \\ r=a=5\text{ cm } \\ {s}^2=(a\mathrm{/}2{)}^2+w^2 \\ s=\sqrt{(a\mathrm{/}2{)}^2+w^2}=\sqrt{(5\mathrm{/}2{)}^2+20^2}\doteq 20.1556\text{ cm } \\ {s}^2=r^2+h^2 \\ h=\sqrt{s^2-r^2}=\sqrt{20.1556^2-5^2}=19.5256\text{ cm} \end{gathered}$$

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