
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 12th, 2009, 01:33 AM  #1 
Newbie Joined: Oct 2009 Posts: 2 Thanks: 0  Comparing perimeter and area of the inscribed polygons
question Use a circle with a radius of 1/2 unit i.e. diameter of 1 unit Compare the perimeter and area of the following inscribed polygon, the circle and the circumscribed polygon for the following i) regular hexagon ii) a regular decagon iii) regular dodecagon iv) a regular icosagon Predict what would happen if you continued to increase the number of sides in the polygon? Test your prediction with a regular polygon of 180 sides. I can probably work out the rest of the polygons if two are shown to me. Help is greatly appreciated Thank you 
October 12th, 2009, 03:33 AM  #2 
Senior Member Joined: Mar 2007 Posts: 428 Thanks: 0  Re: Comparing perimeter and area of the inscribed polygons
You can do a drawing as well as can we, so let's just be descriptive: Divide each polygon into triangles. You don't need to draw them all, just count them to find the total area of the polygon. Use the Angle Sum of a Polygon formula to find each angle. You'll need that and some simple right triangle trig to find other lengths. Use those lengths to calculate what you need, area of triangle, radius of circle, .... You must be given one starting dimension, so use a length of 1 for each side, or you could use a radius of 1 for one of the circles ...the rest is just basic trig using the triangles you drew and the angle found from the Angle Sum formula. Can you submit a drawing showing some effort and we can take it from there? 

Tags 
area, comparing, inscribed, perimeter, polygons 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Area Changes in Irregular Polygons  automan12  Algebra  0  May 30th, 2013 12:32 AM 
Max. area of an inscribed rectangle  tiba  Algebra  3  June 20th, 2012 05:56 AM 
Perimeter & Area Optimization  Chee  Calculus  1  April 1st, 2012 04:47 PM 
area and perimeter  tsl182forever8  Algebra  1  February 28th, 2012 10:58 PM 
Given perimeter, two fields, max area and a cow  frankiee  Algebra  7  February 6th, 2010 07:39 PM 