Answer to Question #115143 in Geometry for gly

Question

in two regular polygons having the same number of sides find the area of smaller if sides have length 4 and 12 and area of larger is 10 260

Answer 1

The area of ​​a regular polygon with the n number of sides n:

S= ((n*a² /4)*сot(π/n)

S₁=?

S₂=10260

а₁=4

а₂=12

S₁/S₂ = a₁²/a₂²

S₁/10260=16/144

S₁=10260*16/144=1140

Answer S₁=1140