Question 810700
The number of sides and number of diagonals in a polygon is related by:  {{{(n^2 - 3n)/2 = d}}} where n is the number of sides and d is the number of diagonals.<P>
{{{n^2 - 3n = 340}}}<P>
{{{n^2 - 3n - 340 = 0}}}<P>
(n+17)(n-20) = 0 so n=-17 or 20.  A polygon can't have a negative number of sides, so n = 20.<P>
One formula for the area of a regular polygon given the number of sides and length of sides is Area = {{{(n*S^2)/4tan(pi/n)}}} where n is the number of sides, S is the length of a side, and TAN is taken in radians.<P>
Area of this polygon = {{{20*(2.4^2)/4tan(pi/20)}}} = approximately 181.8 cubic centimeters.