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Decagon and Dodecagon Areas (Posted on 2010-05-11) Difficulty: 2 of 5
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)

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Solution Solution Comment 3 of 3 |

Let r be the radius of the circle and
n the number of sides of the regular
polygon.
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
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