One moreversionof the perimeterformulaapplieswhenthe polygonis inscribedin a “unit circle,”whichis
a circlewith a radiusof.
Perimeterof a regularpolygonwith sidesinscribedin a unit circle:Example 1
A squarehas a radiusof inches.Whatis the perimeterof the square?Use , with and.Noticethat a side and two radii makea right triangle.The legs are incheslong,and the hypotenuse,whichis a side of the square,is incheslong.Useinches.The purposeof this exampleis not to calculatethe perimeter, but to verifythat the formulasdevelopedabove
“work.”
Areaof a RegularPolygon
The next logicalstep is to completeour studyof regularpolygonsby developingarea formulas.
Take anotherlook at the regularpolygonfigureabove.Here’s how we can find its area,.
Two radii and a side makea trianglewith base and altitude.
- Thereare of thesetriangles.