The number of sides and number of diagonals in a polygon is related by: where n is the number of sides and d is the number of diagonals.
(n+17)(n-20) = 0 so n=-17 or 20. A polygon can't have a negative number of sides, so n = 20.
One formula for the area of a regular polygon given the number of sides and length of sides is Area = where n is the number of sides, S is the length of a side, and TAN is taken in radians.
Area of this polygon = = approximately 181.8 cubic centimeters.