All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Inscribed Octagon (Posted on 2024-06-11) Difficulty: 3 of 5
An octagon which has side lengths 3, 3, 11, 11, 15, 15, 15 and 15 is inscribed in a circle. Find the area of the octagon.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer-aided solution | Comment 1 of 3
The program tries different radii for the circumscribing circle to home in on where the calculated isoscelese triangles (formed from adjacent right triangles) have their apex angles total 360°.


clearvars,clc
side=[ 3, 3, 11, 11, 15, 15, 15,15];

for r= 14.577379737113:.00000000000001:14.577379737114
  totArea=0; totAngle=0;
  for i=1:length(side)
    angle=asind(side(i)/(2*r));
    totArea=totArea+side(i)*cosd(angle);
    totAngle=totAngle+2*angle;
  end
  fprintf('%15.13f %15.13f %15.13f\n',r,totArea,totAngle);
end

is the final version narrowing in on the following inclueded output:

Radius of circle Area of Octagon   Verification of
                                  total central angle
14.5773797371132 77.7917582206420 360.0000000000003
14.5773797371133 77.7917582206420 360.0000000000001
14.5773797371133 77.7917582206420 359.9999999999998
14.5773797371133 77.7917582206420 359.9999999999994

the desired area is 77.7917582206420.

  Posted by Charlie on 2024-06-11 12:44:37
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information