The length of the apothem is 10.9 feet while the area of the floor of the gazebo is 391.1 feet²
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
The perimeter of the floor is 72 feet. Hence:
Side length = (72) / 8 = 9 feet
Half of side length = (9/2) = 4.5 feet. Using Pythagoras, apothem (a):
11.8² = a² + 4.5²
a = 10.9 feet
Area of octagon = 2(1 + √2) * side length² = 2(1 + √2) * 9² = 391.1 feet²
The length of the apothem is 10.9 feet while the area of the floor of the gazebo is 391.1 feet²
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