Hexagonal 13891

A regular hexagonal pyramid has a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. Please sketch the picture. Please calculate the surface of a regular hexagonal pyramid.

Final Answer:

S =  674.2611 cm

Step-by-step explanation:

$$\begin{gathered} r=8\text{cm} \\ a=5=8\text{cm} \\ h=20\text{cm} \\ a=r=8\text{cm} \\ {s}^2=h^2+a^2 \\ s=\sqrt{h^2+a^2}=\sqrt{20^2+8^2}=4\sqrt{29}\text{cm}\doteq 21.5407\text{cm} \\ w=\sqrt{s^2-(a/2{)}^2}=\sqrt{21.5407^2-(8/2{)}^2}=8\sqrt{7}\text{cm}\doteq 21.166\text{cm} \\ {S}_1=3\cdot \sqrt{3}/2\cdot a^2=3\cdot \sqrt{3}/2\cdot 8^2=96\sqrt{3}{\text{cm}}^2\doteq 166.2769{\text{cm}}^2 \\ {S}_2=\frac{a\cdot w}{2}=\frac{8\cdot 21.166}{2}=32\sqrt{7}{\text{cm}}^2\doteq 84.664{\text{cm}}^2 \\ S=S_1+6\cdot S_2=166.2769+6\cdot 84.664=674.2611\text{cm} \end{gathered}$$

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