CK12 - Geometry

Supposea circlehas a radiusof units.

The scalefactorof this circleand the one in the diagramand tableabove,with radius , is ,

or just.

• You knowhow a scalefactoraffectsarea measures.If the scalefactoris , then the area is times

as much.

This meansthat if the area of a circlewith radius is , then the area of a circlewith radius is.

Areaof a CircleFormula

Let be the radiusof a circle,and the area.

You probablynoticedthat the reasoningaboutareahere is very similarto the reasoningin an earlierlesson
whenwe exploredtheperimeterof polygonsand thecircumferenceof circles.

Example 1

A circleis inscribedin a square.Eachside of the squareis cm long.Whatis the area of the circle?

Use. The lengthof a side of the squareis also the diameterof the circle.The radiusis.

The area is.

Areaof a Sector

The area of a sectoris simplyan appropriatefractionalpart of the area of the circle.Supposea sectorof a

circlewith radius and circumference has an arc with a degreemeasureof and an arc lengthof
units.