WHAT IS AREA AXIOMS,CONGRUENT AREA AXIOMS,AREA MONOTONE AXIOM,AREA ADDITION AXIOM AND RECTANGLE AREA AXIOM

The axioms related to area is termed as Area axioms.

There are four types of area axioms:-

$EverypolygonalregionRhasanarea,measureinsquareunitanddenotedbyar\left(R\right)\phantom{\rule{0ex}{0ex}}i)Congruentareaaxiom:If{R}_{1}and{R}_{2}betworegionssuchthat{R}_{1}\cong {R}_{2}thenar({R}_{1})=ar({R}_{2}\left)\phantom{\rule{0ex}{0ex}}ii\right)Areamonotoneaxiom:If{R}_{1}\subset {R}_{2},thenar\left({R}_{1}\right)\le ar\left({R}_{2}\right)\phantom{\rule{0ex}{0ex}}iii)Areaadditionaxiom:If{R}_{1}and{R}_{2}aretwopolygonalregions,whoseintersectionisafinitenumberofpoints\phantom{\rule{0ex}{0ex}}andlinesegmentsandR={R}_{1}\cup {R}_{2},thenar(R)=ar({R}_{1})+ar({R}_{2}\left)\phantom{\rule{0ex}{0ex}}iv\right)Rec\mathrm{tan}gularareaaxiom:Asthenamesuggestsitistheaxiomrelatedtoareaofrec\mathrm{tan}gle\phantom{\rule{0ex}{0ex}}IfAB=ametreandAD=bmetre,thenar(rec\mathrm{tan}gularregionABCD)=absquaremetre$

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