Math CentralQuandaries & Queries


Help please. I am building an octagon tree house to live in. I would like the total square footage to equal 800 to 1,000 sq ft. How long should each side of the octagon be.
tx, susan

Hi Susan,

I assume you want a regular octagon.

If you look at our page on finding the area of a regular polygon you will see a formula that Stephen developed that uses the length of a side $a$ and the number of sides $n.$ the expression is

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

If you want the area to be 800 square feet then this gives

\[800 = \frac{8 \times a^2 }{4 \tan\left(\frac{360^o}{16}\right)}.\]

Use your calculator to calculate $\tan\left(\frac{360^o}{16}\right)$ and then solve for $a.$

Write back if you need more assistance.


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