 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Decagon and Dodecagon Areas (Posted on 2010-05-11) The area of a regular decagon inscribed in a circle is 10 square units.

What is the area of the regular decagon circumscribed about the circle? How about the area of the regular dodecagon circumscribed about the circle?

 No Solution Yet Submitted by K Sengupta Rating: 1.5000 (2 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Solution Comment 3 of 3 | `Let r be the radius of the circle andn the number of sides of the regularpolygon.`
`Area of Inscribed Regular Polygon:`
`   n*r^2*sin(360/n)/2`
`Area of Cicumscribed Regular Polygon:`
`   n*r^2*tan(180/2)`
`Inscribed Regular Decagon:`
`   10*r^2*sin(36)/2 = 10`
`          or`
`   r^2 = 2/sin(36) ~= 3.4026`
`Circumscribed Regular Decagon:`
`   10*[2/sin(36)]*tan(18) ~= 11.0557`
`Circumscribed Regular Dodecagon:`
`   12*[2/sin(36)]*tan(15) ~= 10.9407`
` `

 Posted by Bractals on 2010-05-12 17:06:50 Please log in:

 Search: Search body:
Forums (1)