Quandaries and Queries


I am a parent.
The level of the question secondary (10-12)

I want to build a octagonal deck. The wood I am using are cut in 8 foot lenghts. What I want to know is if the sides of the octagonal are 8 feet, what is the diameter. Also what are the angles of each side?

Your help is greatly appreciatted.



Hi Scott,

From the diagram you can see that d = 8 + 2x feet, where d is the diameter.

Thus if you can find x then d is easy to calculate. Triangle ABC is a right triangle, so by Pythagoras' Theorem

x2 + x2 = 82 = 64


2 x2 = 64 and x2 = 32.


x = √32 = 4 √2


d = 8 + 2x = 8 + 8 √2 = 19.3137 feet

which is approximately 19 feet 3 3/4 inches.

The angle calculation you can find in the answer to a previous question.



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