If two regular polygon of n and 2n sides have the same perimeter their areas are in the ratio: A 2 cosπ/n : 1-cos π/n b 2 cos π/n : 1+cosπ/ n C 2 sin π/n : 1+ cos π/n d 2 sin π/n : 1-cosπ/n

Dear Student,
Please find below the solution to the asked query:

Let side of polygon of n sides be x and that of 2n sides be q.According to questionnx=2nyxy=2...iArea of regular polygon of side a uints and n sides  =12×Perimeter×a2cotπnHenceArea of polygon of n sides=A1=12×nx×x2cotπnArea ofpolygon of 2n sides=A2=12×2ny×y2cotπ2nA1A2=x2cotπn2y2cotπ2nUse iA1A2=4cotπn2cotπ2nA1A2=2cotπncotπ2n=2cosπn.sinπ2ncosπ2n.sinπn= 2cosπn.sinπ2ncosπ2n.2sinπ2n.cosπ2nsin2A=2sinAcosA=cosπncos2π2n=2cosπn1+cosπn cos2A=1+cos2A2

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • 4
What are you looking for?