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By splitting the following figures into rectangles, find their areas$( The\ measures\ are\ given\ in\ centimetres)$.
"
Given: Figures are given.
To do: To find the area by splitting the given figures into rectangle.
Solution:
$( a)$. Here, we can split the given figure into four rectangles.
$ABCM,\ MDLJ,\ KLEI,\ and\ FGHI $
In rectangle $ABCM$,
$AB=4\ cm$
$BC=2\ cm$
$CM=4\ cm$
$AM=BC=2\ cm$
Area of the rectangle $ABCM=4\times2=8\ cm^{2}$
In rectangle $MDLJ$,
$MD=LJ=CM+CD=4+2=6\ cm$ [$\because\ CM=AB=4\ cm\ and\ CD=2\ cm$]
$MJ=DL=AJ-AM=3-2=1$
$\therefore$ Area of the rectangle $( MDLJ)=6\times1=6\ cm^{2}$
In rectangle $KLEI$,
$LE=KI=DE-DL=3-1=2\ cm$
$KL=EI=LJ-KJ=6-3=3\ cm$
Area of the rectangle $( KLEI)=2\times3=6\ cm^{2}$
In rectangle $FGHI$,
$FG=HI=4-3=1\ cm$
$GH=FI=FE+EI=1+3=4\ cm$
Area of the rectangle$( FGHI)=4\times1=4\ cm^{2}$
Total area$=$Sum of the areas of all four rectangle$=8+6+6+4=24\ cm^{2}$
$( b)$. By splitting the given figure into rectangles, we have three rectangles $ABIH,\ FGIJ\ and\ CDEJ$.
In rectangle $ABIH$,
$AB=3\ cm$
$AH=1\ cm$
$\therefore$ Area of the rectangle$( ABIH)=3\times1=3\ cm^{2}$
In rectangle $FGIJ$,
$FG=3\ cm$
$IG=JF=JE-EF=3-2=1\ cm$
Area of the rectangle $( FGIJ)=3\times1=3\ cm^{2}$
In rectangle $CDEJ$,
$CD=3\ cm$
$ED=3\ cm$
Area of the rectangle $( CDEJ)=3\times3=9\ cm^{2}$
$\therefore$ Total area of the figure$=$sum of the areas of all three rectangles$=3+3+9=15\ cm^{2}$
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