Question 549453
An octagon has an area of 100”, it’s [sic] side length is 5, find it’s [sic] apothem. 
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I assume you mean 100 square inches.
Assuming it's a regular octagon, each central angle is 45 degs, and the area of each triangle formed by the radii is 1/8 of the 100 sq inches = 12.5 sq inches.
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Area = 12.5 = b*h/2 = 5*h/2 (h is the apothem)
h = 5
That won't work.
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Area of an octagon with sides of 5 is
{{{ns^2*cot(180/n)/4 = 8*25*cot(22.5)/4}}}
Area =~ 120.71 sq inches
It can't be an octagon with sides = 5 and area = 100.
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PS  it's = it is