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

Correct answer:

S =  30.7768
x = C

Step-by-step explanation:

n=10 a=2  α=2 n2π=2 102 3.14160.3142  tan α = a/2 : h h=a/2/tanα=2/2/tan0.31423.0777  S1=2a h=22 3.07773.0777  S=n S1=10 3.0777=30.7768

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