Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Polygon
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
====Regular polygons==== Many specialized formulas apply to the areas of [[regular polygon]]s. The area of a regular polygon is given in terms of the radius ''r'' of its [[inscribed circle]] and its perimeter ''p'' by :<math>A = \tfrac{1}{2} \cdot p \cdot r.</math> This radius is also termed its [[apothem]] and is often represented as ''a''. The area of a regular ''n''-gon can be expressed in terms of the radius ''R'' of its [[circumscribed circle]] (the unique circle passing through all vertices of the regular ''n''-gon) as follows:<ref>[https://www.mathopenref.com/polygonregularareaderive.html Area of a regular polygon β derivation] from Math Open Reference.</ref><ref>A regular polygon with an infinite number of sides is a circle: <math>\lim_{n \to +\infty} R^2 \cdot \frac{n}{2} \cdot \sin \frac{2\pi}{n} = \pi \cdot R^2</math>.</ref> :<math>A = R^2 \cdot \frac{n}{2} \cdot \sin \frac{2\pi}{n} = R^2 \cdot n \cdot \sin \frac{\pi}{n} \cdot \cos \frac{\pi}{n}</math>
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)