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Find the area of the green figure:
"
To do: To find the are of the green figure.
Solution:
Let $x$ and $y$ are the sides of the green figure.
In rectangle $FCBG$:
Length$=FC=CE-EF=9-x$
Breadth$=FG=HE=y$
Area of the rectangle $FCBG=(9-x)y=32$ [given area$=32\ cm^2$]
$\Rightarrow 9y-xy=32$
$\Rightarrow xy=9y-32\ ...............\ ( i)$
In rectangle $DEHA$
Length of the rectangle $=AH=AG-GH=8-x$
Breadth$=AD=HE=y$
Area of the rectangle $DEHA=( 8-x)y=25$
$\Rightarrow 8y-xy=25$
$\Rightarrow 8y-9y+32=25$ [$\because xy=9y-32$ from $( i)$]
$\Rightarrow -y=25-32=-7$
$\Rightarrow y=7$, Put this value in (i),
$7x=9\times7-32$
$\Rightarrow 7x=63-32$
$\Rightarrow 7x=31$
$\Rightarrow x=\frac{31}{7}$.
Therefore, area of the green figure$=xy=7\times\frac{31}{7}=31\ cm^2$
Thus, area of the green figure is $31\ cm^2$.
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