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 =  30.777
x = (Correct answer is: C) Wrong answer

Solution:

n=10 a=2  α=2π2⋅ n=2⋅ 3.14162⋅ 10≐0.3142  tan⁡α=a/2:h h=a/2/tan⁡(α)=2/2/tan⁡(0.3142)≐3.0777  S1=a⋅ h2=2⋅ 3.07772≐3.0777  S=n⋅ S1=10⋅ 3.0777=30.777n=10 \ \\ a=2 \ \\ \ \\ α=\dfrac{ 2 \pi }{ 2 \cdot \ n }=\dfrac{ 2 \cdot \ 3.1416 }{ 2 \cdot \ 10 } \doteq 0.3142 \ \\ \ \\ \tan α=a/2 : h \ \\ h=a/2 / \tan(α)=2/2 / \tan(0.3142) \doteq 3.0777 \ \\ \ \\ S_{1}=\dfrac{ a \cdot \ h }{ 2 }=\dfrac{ 2 \cdot \ 3.0777 }{ 2 } \doteq 3.0777 \ \\ \ \\ S=n \cdot \ S_{1}=10 \cdot \ 3.0777=30.777
x=Cx=C

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