Answer:
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
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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.