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in Trigonometry by (53.1k points)

If the number of sides of two regular polygons having the same perimeter be n and 2n, respectively, their areas are in the ratio

(A)  2 cos(π/n)/cosπ/2n)

(B)  2 cos(π/n)/1 + cos(π/n)

(C)  cos(π/n/sin(π/n))

(D) None of these 

1 Answer

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by (53.3k points)
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Best answer

Correct option  (B)  2 cos(π/n)/1 + cos(π/n)

Let s be the perimeter of both the polygons. Then the length of each side of the first polygon is s/n and that of second polygon is s/2n.

If A1, A2 denote their areas, then

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