centralanglesinto two congruenthalves;eachof thesehalf anglesmeasures
.
UsingTrigonometrywith the RegularPolygon
Recallthat in a right triangle:
sine of an angle= cosineof an angle=
In the diagramabove,for the half anglesmentioned,
is the lengthof the oppositesideis the lengthof the adjacentsideis the lengthof the hypotenuseNow we can put thesefactstogether:
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Perimeterof a RegularPolygon
We continuewith the regularpolygondiagrammedabove.Let be the perimeter. In simplestterms,
Hereis an alternateversionof the perimeterformula.
Perimeterof a regularpolygonwith sidesand a radius unitslong: