SOLUTION: (The gazebo is octagonal.) 1.) 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

Question 1160997: (The gazebo is octagonal.)
1.) 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?
2.) To make the floor perfectly regular you need to make sure to cut the wood at the
correct angle on the ends. What is the measure of the angle at each corner of the gazebo?
( for the first answer on number one , I got 174 square feet for the area.)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The sum of the measures of the interior angles of any convex polygon is given by:

where

is the number of vertices.

Since the polygon you are describing is equilateral, it must also be equiangular, hence each interior angle must have a measure that is the sum of the measures the sum of the interior angles divided by the number of vertices.

For

, each interior angle measures

degrees.

Note that any line segment with endpoints at the center of the octagon and a vertex of the octagon bisects the interior angle, hence the end of each piece of wood must be cut at an angle measuring one-half of the interior angle measure.

John

My calculator said it, I believe it, that settles it

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