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A regular octagon with side lengths of 5.5 inches has an apothem length of 3 inches

What is the area of this figure in square inches

 May 4, 2020
 #1
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The area of a regular octagon is given by the formula \(A = 2s^2(1 + \sqrt{2})\), where \(s\) is the side length of the octagon.

 

We know that \(s = 5.5\text{ in}\), so we just plug in that value into the equation to get:

 

\(A = 2(5.5^2)(1 + \sqrt{2})\)

 

\(A = 60.5(1 + \sqrt{2})\)

 

\(A = 60.5 + 60.5(1.414)\)

 

\(A = 60.5 + 85.547 = \fbox{$146.047 \text{ in}^2$}\) :D

 May 4, 2020
 #2
avatar+337 
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I thought it was just 60 inches^2

 May 4, 2020

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