My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
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
magician is offline  
 
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?
David is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

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





Copyright © 2019 My Math Forum. All rights reserved.