Difference between revisions of "Octagon"

Revision as of 17:59, 8 September 2007

An octagon is an eight-sided polygon.

Each internal angle of a regular octagon measures 135 degrees, so the sum of the angles is $1080^{\circ}$ .

Area: $\displaystyle 2s^2(1 + \sqrt{2})$

Apothem: $\frac{s(1+ \sqrt2 )}{2}$

Inradius: $\frac{s(1+ \sqrt2 )}{2}$

Circumradius: $\frac{s\sqrt{4+2\sqrt{2}}}{2}$

This article is a stub. Help us out by expanding it.

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 Each internal [[angle]] of a [[Regular polygon | regular]] octagon measures 135 [[degree (geometry) | degrees]], so the sum of the angles is <math>1080^{\circ}</math>.
-[[Area]]: <math>\displaystyle 2s^2(\sqrt{2} + 1)</math>
+[[Area]]: <math>\displaystyle 2s^2(1 + \sqrt{2})</math>
-[[Apothem]]: <math>\frac{s(\sqrt{2} + 1)}{2}</math>
+[[Apothem]]: <math>\frac{s(1+ \sqrt2 )}{2}</math>
-[[Inradius]]: <math>\frac{s(\sqrt{2} + 1)}{2}</math>
+[[Inradius]]: <math>\frac{s(1+ \sqrt2 )}{2}</math>
-[[Circumradius]]:  <math>s\sqrt{1 + \frac{\sqrt{2}}{2}}</math>
+[[Circumradius]]:  <math>\frac{s\sqrt{4+2\sqrt{2}}}{2}</math>
 {{stub}}