Find the

Find the content of a regular 12 sided polygon if its side a = 12 cm.

Correct answer:

S =  1612.2459 cm²

Step-by-step explanation:

$$\begin{gathered} a=12\text{ cm } \\ n=12 \\ A=360\mathrm{/}n=360\mathrm{/}12=30\text{ ° } \\ \tan A\mathrm{/}2={\displaystyle \frac{a\mathrm{/}2}{h}} \\ h=(a\mathrm{/}2)\mathrm{/}\tan (A\mathrm{/}2)=(12\mathrm{/}2)\mathrm{/}\tan (30\mathrm{/}2)\doteq 22.3923\text{ cm } \\ {S}_1={\displaystyle \frac{h\cdot a}{2}}={\displaystyle \frac{22.3923\cdot 12}{2}}\doteq 134.3538{\text{m}}^2 \\ S=n\cdot S_1=12\cdot 134.3538=1612.2459{\text{cm}}^2 \end{gathered}$$

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