The area of the sector(pattern)is = sq in.LessonSummary
We usedthe idea of a limit againin this lesson.Thatenabledus to find the areaof a circleby studying
polygonswith moreand moresides.Our approachwas very similarto the one usedearlierfor the circum-
ferenceof a circle.Oncethe area formulawas developed,the area of a sectorwas a simplematterof taking
the properfractionalpart of the wholecircle.
Summaryof Formulas:
AreaFormula
Let be the radiusof a circle,and the area.Areaof a Sector
A circlehas radius. A sectorof the circlehas an arc with degreemeasure and arc length units.The area of the sectoris squareunits.Pointsto Consider
Whenwe talk abouta limit,for examplefindingthe limit of the areasof regularpolygons,how manysides
do we meanwhenwe talk about“moreand more?”As the polygonshavemoreand moresides,what happens
to the lengthof eachside?Is a circlea polygonwith an infinitenumberof sides?And is each“side”of a
circleinfinitelysmall?Now that’s small!
In the next lessonyou’llsee wherethe formulacomesfrom that givesus the areasof regularpolygons.This
is the formulathat was usedto producethe tableof areasin this lesson.
LessonExercises
Completethe tableof radii and areasof circles.Expressyour answersin termsof.
Radius Area(units) (squareunits)