CK12 - Geometry

To find the area,you needto counthow manyof thesecirclesfit into the rectangle,includingpartsof circles.

So far you can see that the rectangle’s spaceis madeup of wholecircles.Determiningthe fractional
partsof circlesthat wouldcoverthe remainingwhitespaceinsidethe rectanglewouldbe no easyjob! And
this is just for a very simplerectangle.The challengeis evenmoredifficult for morecomplexshapes.

Insteadof fillingspacewith circles,peoplelong ago realizedthat it is muchsimplerto use a squareshape

for a unit of area.Squaresfit togethernicelyand fill spacewith no gaps.The squarebelowmeasures foot

on eachside,and it is called squarefoot.

Now it’s an easyjob to find the area of our rectangle.

The area is squarefeet, because is the numberof unitsof area (squarefeet) that will exactlyfill, or
cover, the rectangle.

The principlewe usedin Example1 is moregeneral.

Theareaof a two-dimensionalfigureis the numberof squareunitsthat will fill, or cover, the figure.

Two AreaPostulates

CongruentAreasIf two figuresare congruent,they havethe samearea.