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 answer:

h =  19.5256 cm

Step-by-step explanation:

$$\begin{gathered} a=5\text{ cm } \\ w=20\text{ cm } \\ {h}_2=\sqrt{3}\mathrm{/}2\cdot a=\sqrt{3}\mathrm{/}2\cdot 5\doteq 4.3301\text{ cm } \\ {w}^2=h_2^2+h^2 \\ h=\sqrt{w^2-h_2^2}=\sqrt{20^2-4.3301^2}=19.5256\text{ cm} \end{gathered}$$

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