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Question
A gazebo in the shape of a regular octagon has equal sides of 9 feet and an apothem of 10.9 feet. Find the cost of the gazebo’s floor if the flooring costs $3 per square foot. Round to the nearest hundred dollars.
Solution
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The area of a regular polygon is the product of the length of the apothem and the perimeter, divided by 2.
The perimeter is the sum of the lengths all sides. An octagon has 8 sides, thus a regular octagon has 8 sides with equal length.
We can then determine the area of the regular polygon:
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