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| Math Central | Quandaries & Queries |
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Question from mark, a parent: I need to know the measurements of an octagon with a inside diameter of 34.5 inches from side to side |
Hi Mark,
Suppose the distance from side to side of a regular octagon is d units and the length of a side is s units.
From the diagram d = s + 2x. Triangle ABC is a right triangle so Pythagoras theorem states that
s2 = x2 + x2 = 2x2
or
x = s/√2
Thus
d = s + 2x = s + 2s/√2 = s(1 + 2/√2) = (1 + √2) s
or
s = 1/(1 + √2) d
Penny
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