The length of one side of the octagon is given by: Then, the apothem can be determined using the Pythagorean theorem in the following way: Clearing to have: Then, the area is given by: Where, L: length of the octagon sides a: apotema Substituting values: Answer: the approximate length of the apothem is: a = 10.91 feet The approximate area of the floor of the gazebo is: A = 392.76 feet ^ 2