Question 1165390
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Picture the regular octagon as the 28-inch square, with isosceles right triangles cut off each corner.<br>
If s is the length of each side of the octagon, then each leg of each of the isosceles triangles is {{{s/sqrt(2)}}}.<br>
Then the 28-inch side of the square is composed of the legs of two of the isosceles triangles and one side of the octagon.  Its length is<br
{{{s+2(s/sqrt(2)) = s+s*sqrt(2) = s(1+sqrt(2))}}}<br>
So<br>
{{{s(1+sqrt(2)) = 28}}}
{{{s = 28/(1+sqrt(2))}}}<br>
Use a calculator and round as directed.<br>