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Question

If a regular pentagon and regular decagon have the same perimeter and A1,A2 are areas of regular pentagon and regular decagon respectively then A1A2 is

A
45
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B
54
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C
25
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D
52
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Solution

The correct option is C 25
Area of polygon =na24cotπn where a is side of regular polygen
[5a1=10a2 (given)]a1=length of penttagona2=length of decagon
A1=5a214cotpi5
A2=10a224cotπ10
A1A2=25

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