Which

Which of the following numbers is the most accurate 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

Correct answer:

S =  30.7768
x = C

Step-by-step explanation:

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

$x=C$

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