Question 629548
<pre>
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 

     {{{(n(n-1))/2}}} - 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 = {{{(s^2*n)/(4tan("180°"/n))}}}, where s = lebgth of a side and
n = the number of sides.

Area = {{{(2.4^2*20)/(4tan("180°"/20))}}}

Area = {{{(5.76*20)/(4tan("9°"))}}}

Area = {{{(5.76*20)/(4tan("9°"))}}}

Area = 181.8360436 cm²

Edwin</pre>