Circumscribed 22713

Calculate the circumference and the area of a regular ten-angle polygon if the radius of the circumscribed circle r = 20 cm.

Correct answer:

S =  1175.5705 cm2
o =  123.6068 cm

Step-by-step explanation:

R=20 cm n=10  A=360/n=360/10=36 ∘  sin A/2 =  Ra/2​  a=2⋅ R⋅ sin(A/2)=2⋅ 20⋅ sin(36/2)≐12.3607 cm  r=R2−(a/2)2​=202−(12.3607/2)2​≐19.0211 cm  S1​=2r⋅ a​=219.0211⋅ 12.3607​≐117.5571 cm2 S=n⋅ S1​=10⋅ 117.5571=1175.5705 cm2
o=n⋅ a=10⋅ 12.3607=123.6068 cm

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