Decagon prism

A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm³, round to two decimal places.

Correct result:

V =  61.5537 cm³

Solution:

$$\begin{gathered} a=2\text{ cm } \\ h=a=2=2\text{ cm } \\ n=10 \\ S=n\mathrm{/}4\cdot a^2\mathrm{/}\tan (\pi \mathrm{/}n)=10\mathrm{/}4\cdot 2^2\mathrm{/}\tan (3.1416\mathrm{/}10)\doteq 30.7768{\text{cm}}^2 \\ V=S\cdot h=30.7768\cdot 2=61.5537{\text{cm}}^3 \end{gathered}$$

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