Find the area of the shaded region in $Fig.$
Find the area of the shaded region in $Fig.$
join $GH$ and $FE$
Here, breadth of the rectangle $B C=12 \,m$
$\therefore$ Breadth of the inner rectangle $E F G H=12-(4+4)=4 \,cm$
which is equal to the diameter of the semi-circle $EJF,$ $d=4\,m$
$\therefore$ Radius of semi-circle $EJF,$ $r=2\, m$
$\therefore$ Length of inner rectangle $E F G H=26-(5+5)=16 \,m$
$\therefore$ Area of two semi-circles $E J F$ and $H I G=2\left(\frac{\pi r^{2}}{2}\right)=2 \times \pi \frac{(2)^{2}}{2}=4 \pi\, m$
Now, area of inner rectangle $E F G H=E H \times F G=16 \times 4=64\, m ^{2}$
and area of outer rectangle $A B C D=26 \times 12=312 \,m ^{2}$
$\therefore$ Area of shaded region $=$ Area of outer rectangle $-$ (Area of two semi-circles $+$ Area of inner rectangle)
$=312-(64+4 \pi)=(248-4 \pi) \,m ^{2}$
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