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 answer:

V =  61.5537 cm³

Step-by-step explanation:

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

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