Question 630017
<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 = 35 

     {{{(n(n-1))/2}}} - n = 35
     
     n(n-1) - 2n = 70

     nē - n - 2n - 70 = 0

     nē - 3n - 70 = 0
   
     (n - 10)(n + 7) = 0

      n = 10,  n = -7, which we discard.

So the regular polygon has 10 sides.

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

Area = {{{na^2tan("180°"/n)}}}, where a = apothem and 
n = the number of sides.

Area = {{{10*10^2tan("180°"/10)}}}

Area = {{{(10*100*tan("18°"))}}}

Area = {{{(1000)*tan("18°"))}}}

Area = 324.9196962 square units of area

Edwin</pre>