1) Given a regular octagon has a side length of \(12\) units, determine the length of the apothem and the area of the octagon to the nearest hundredth.
2) Given an equiangular triangle with an area of \(60\) units\(^2\), determine the length of the apothem and the radius of the triangle to the nearest hundredth.
2) Given an equiangular triangle with an area of \(60\) units\(^2\), determine the length of the apothem and the radius of the triangle to the nearest hundredth.
4) One regular hexagon is inscribed in a circle and another is circumscribed about the same circle. If the radius of the circle is \(9\) units, determine the ratio of the area of the smaller hexagon to the larger one.
7) If a regular pentagon has a side length of \(19\) units, what would the side length of a regular heptagon have to be in order to have the same area as the pentagon? Round answer to the nearest hundredth.