SOLUTION: fine the area of a regular dodecagon with side 10 cm

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Question 36682: fine the area of a regular dodecagon with side 10 cm
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
A dodecagon is a 12-sided polygon.

The area of a regular polygon of 'n'-sides with each side = 'a' is given by
A+=+n%2Aa%5E2%2Acot%28pi%2Fn%29%2F4

For a regular dodecagon with each side 10 cm, the area is
A+=+12%2A10%5E2%2Acot%28pi%2F12%29%2F4
or A+=+300%2Acot%2815%5Eo%29
or A = 300 x 3.732 = 1119.6

Hence the reqd. area is 1119.6cm%5E2.