CK12 - Geometry

b.Whatis the scalefactorrelatingthe rhombi?

The scalefactorrelatingthe smallerrhombusto the largerone is

c.Whatis the perimeterof eachrhombus?

Answer

• Perimeterof smallerrhombus


• Perimeterof largerrhombus

d.Whatis the ratio of the perimeters?

e.Whatis the area of eachrhombus?

Areaof smallerrhombus=

Areaof largerrhombus=

Whatdo you noticein this example?The perimetershavethe sameratio as the scalefactor.

But whataboutthe areas?The ratio of the areasis certainlynotthe sameas the scalefactor. If it were,the

area of the largerrhombuswouldbe , but the area of the largerrhombusis actually

WhatISthe ratio of the areas?

The ratio of the areasis Noticethat or in decimal,.

So at leastin this casewe see that the ratio of the areasis thesquareof the scalefactor.

ScaleFactorsand Areas

Whathappenedin Example1 is no accident.In fact, this is the basicrelationshipfor the areasof similar
polygons.

Areasof SimilarPolygons

If the scalefactorrelatingthe sidesof two similarpolygonsis , then the area of

the largerpolygonis timesthe area of the smallerpolygon.In symbolslet the area

of the smallerpolygonbe and the area of the largerpolygonbe. Then: