Decagon

Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m

Correct result:

S =  2.9389 m2
o =  6.1803 m

Solution:

R=1 m n=10  A=360/n=360/10=36∘  sin⁡A/2=a/2R  a=2⋅ R⋅ sin⁡(A/2)=2⋅ 1⋅ sin⁡(36/2)≐0.618 m  r=R2−(a/2)2=12−(0.618/2)2≐0.9511 m  S1=r⋅ a2=0.9511⋅ 0.6182≐0.2939 m2 S=n⋅ S1=10⋅ 0.2939=2.9389 m2
o=n⋅ a=10⋅ 0.618=6.1803 m

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