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##### How do you find the length of an apothem of a hexagon

 Mathematics Tutor: None Selected Time limit: 1 Day

I was only given the length of one side of the regular hexagon. I would like step by step on how to complete this. the side length was 22

Mar 27th, 2015

The apothem is the line from the center of the hexagon to the middle of any side.

Since each side of a hexagon is the base of an equilateral triangle, then the apothem is really just the ALTITUDE of the equilateral triangle.

If the side is 22, the the altitude divide the base into two equal segments, both 11.

So, then the apothem would be found by

tan 60 = apothem / 11

apothem = 11tan60

= 19.05

Mar 27th, 2015

How did you get that final answer? do you divide those two numbers?

Mar 27th, 2015

draw an equilateral triangle.  The altitude is the apothem.

notice that it divide the triangle into 2 RIGHT TRIANGLES.

The base angle is 60 because the whole triangle is an equilateral.

Then just use the relationship of tan = opposite side / adjacent side.

That gives you tan60 = apothem / 11

solve from there.

Does that clear it up?

Mar 27th, 2015

yes. thank you very much.

Mar 27th, 2015

you're welcome :)

Mar 27th, 2015

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Mar 27th, 2015
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Mar 27th, 2015
Dec 9th, 2016
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