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October 12th, 2009, 01:33 AM   #1
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Comparing perimeter and area of the inscribed polygons


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
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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?
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