CK12 - Geometry

• Find the areasof regularpolygonswith radius.


• Let the polygonshavemoreand moresides.


• See if a limit showsup in the data.


• Use similarityto generalizethe results.

The details:

Beginwith polygonshaving and sides,inscribedin a circlewith aradiusof.

Now imaginethat we continuedinscribingpolygonswith moreand moresides.It wouldbecomenearlyim-
possibleto tell the polygonfrom the circle.The tablebelowshowsthe resultsif we did this.

RegularPolygonsInscribedin a Circlewith Radius

Numberof sidesof polygon Areaof polygon

As the numberof sidesof the inscribedregularpolygonincreases,the area seemsto approacha “limit.”

This limit is approximately , whichis.

Conclusion:The area of a circlewith radius is.

Now we extendthis idea to othercircles.You knowthatall circlesare similarto eachother.