SOLUTION: a regular polygon has 170 diagonals and 2.4cm side length. what is its area?

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Question 629548: a regular polygon has 170 diagonals and 2.4cm side length. what is its area?
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
There are n vertices, there are C(n,2) ways to connect 2 of them.
All of these represent diagonals except the n sides, so the number
of diagonals is

     C(n,2) - n = 170 

     %28n%28n-1%29%29%2F2 - n = 170
     
     n(n-1) - 2n = 340

     n² - n - 2n - 340 = 0

     n² - 3n - 340 = 0
   
     (n - 20)(n + 17) = 0

      n = 20,  n = -17

So the regular polygon has 20 sides.

The formula for the area of an n-sided regular polygon is

Area = %28s%5E2%2An%29%2F%284tan%28%22180%B0%22%2Fn%29%29, where s = lebgth of a side and
n = the number of sides.

Area = %282.4%5E2%2A20%29%2F%284tan%28%22180%B0%22%2F20%29%29

Area = %285.76%2A20%29%2F%284tan%28%229%B0%22%29%29

Area = %285.76%2A20%29%2F%284tan%28%229%B0%22%29%29

Area = 181.8360436 cm²

Edwin