If the number of sides of two regular polygons having the same prerimeter be `n and 2n` respectiely, prove that their areas are in the ratio `2cos pi/n: (1+cos pi/n)`

The area of the circle and the area of a regular polygon of n sides and of perimeter equal to that of the circle are in the ratio of tan((pi)/(n)):(pi)/(n)(b)cos((pi)/(n)):(pi)/(n)sin(pi)/(n):(pi)/(n)(d)cot((pi)/(n)):(pi)/(n)

The area of the circle and the area of a regular polygon of n sides and the perimeter equal to the circle are in the ratio of

Consider the following statements : 1. If n ge 3 and mge3 are distinct positive integers, then the sum of the exterior angles of a regular polygon of m sides is different from the sum of the exterior angles of a regular polygon of n sides. 2. Let m, n be integers such that m gt n ge 3 . Then the sum of the interior angles of a regular polygon of m sides is greater than the sum of the interior angles of a regular polygon of n sides, and their sum is (m+n)(pi)/(2) . Which of the above statements is/are correct?

Prove that the area of a regular polygon hawing 2n sides,inscribed in a circle,is the geometric mean of the areas of the inscribed and circumscribed polygons of n sides.

If phi be the exterior angle of a regular polygon of n sides and theta is any constant, then prove that costheta+cos(theta+phi)+cos(theta+2phi)+…+to n term =0

An exterior angle of a regular polygon having n sides is more than that of the polygon having n^2 sides by 50^@ . Then find the number of the sides of each polygon