First you need to know the total area of the floor so you can determine how much
wood to buy. If each side of the gazebo is 6 feet long and the length of the apothem is
7.25 feet, what is the area of the floor

  174 square feet

Step-by-step explanation:

The perimeter of the gazebo is the product of the side length and the number of sides.

  P = ns = 8(6 ft) = 48 ft

Then the area is ...

  A = (1/2)Pa = (1/2)(48 ft)(7.25 ft) = 174 ft²

Comment on the number of sides

The number of sides of this gazebo is not given. However, we can figure the central angle involved. It will be given by ...

  α = 2·arctan(s/(2a)) = 2·arctan(6/14.5) ≈ 45°

Then the number of sides is 360°/45° = 8.