Math CentralQuandaries & Queries


Question from Jan:

Lot size is 30' by 30' will a 1,165sq ft. Octagon home fit on lot? I don't know the wall size's only the total size of building? Thank You for have this?
If this won't fit what size in sq ft will fit?

Hi Jan,

A while ago Stephen developed an expression for the area $A_{RP}$ of a regular polygon with $n$ sides and side length $a$ units. his expression is

\[A_{RP} = \frac{a^2 n}{4 \tan\left(\frac{360^o}{2 n}\right)}\]

You know that $n = 8$ and $A_{RP} = 1,165$ square feet and hence you can solve for $a.$ I got $a = 15.53$ feet but you should check my calculations.

I think you are interested in the width of the octagon. In this response Stephen shows that the width $w$ is related to the side length $a$ by

\[a = 0.4142w\]

(Stephen uses $x$ where I have used $a.$)

I hope this helps,

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