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Q.

Find the length of the perimeter of a regular decagon which surrounds a circle of radius 12cm.


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a

60 cm

b

66 cm

c

72 cm

d

78 cm 

answer is D.

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Detailed Solution

Given that the decagon surrounds the circle.
radius of the in-circle, r = 12 cm
Side of the regular decagon is n=10
Let, length of the regular decagon be l.
l=2rtan180∘n=2×12×tan180∘10=24×tan18∘=24×0.32492=7.79 cm
∴ Perimeter =10l ≈ 78 cm
 
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