The length of the apothem is 10.9 feet and the area of the gazebo floor is 392.7 ft²
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 the side length is 72/8 = 9 feet. Let a represent the apothem.
Using Pythagoras theorem:
11.8² = a² + (9/2)²
a = 10.9 feet
area of octagon = perimeter * apothem / 2 = 72 * 10.9/2 = 392.7 ft²
The length of the apothem is 10.9 feet and the area of the gazebo floor is 392.7 ft²
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