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### Sides of an Octagon

```
Date: 04/13/97 at 11:35:29
From: Jeremy Gilick
Subject: Octagon sides

What is the formula for the length of the sides of an octagon whose
diameter is 15 feet?  I've tried to find a formula but can't seem to
find one.
```

```
Date: 04/13/97 at 18:19:30
From: Doctor Steven
Subject: Octagon sides

You can draw eight congruent triangles emanating from the center of
the octagon.  These eight triangles should be isosceles and and each
will have a central angle of 45 degrees.  This means the other two
angles in each triangle will be 67.5 degrees.  The two like sides of
each triangle are the radius of the octagon, or 7.5 feet.

Use your knowledge of triangles to find the height of these triangles
and that will be your distance from the center of the octagon to the
center of the sides. Find the length of the third side of the triangle
and that is the length of the sides of the octagon.

-Doctor Steven,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

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