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) 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=30.7768
x=Cx=C

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