Which

Which of the following numbers most accurately area of a regular decagon with side s = 2 cm?

(A) 9.51 cm²
(B) 20 cm²
(C) 30.78 cm²
(D) 31.84 cm²
(E) 32.90 cm²

Result

S =  30.7768
x = (Correct answer is: C)

Step-by-step explanation:

$$\begin{gathered} n=10 \\ a=2 \\ \alpha ={\displaystyle \frac{2\pi }{2\cdot n}}={\displaystyle \frac{2\cdot 3.1416}{2\cdot 10}}\doteq 0.3142 \\ \tan \alpha =a\mathrm{/}2:h \\ h=a\mathrm{/}2\mathrm{/}\tan (\alpha )=2\mathrm{/}2\mathrm{/}\tan (0.3142)\doteq 3.0777 \\ {S}_1={\displaystyle \frac{a\cdot h}{2}}={\displaystyle \frac{2\cdot 3.0777}{2}}\doteq 3.0777 \\ S=n\cdot S_1=10\cdot 3.0777=30.7768 \end{gathered}$$

$x=C$

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