Question

Find the area of the shaded region given in figure if the diameter of all the four semicircles is $4cm$.

Answer 1

Total area of ABCD square $=s\times s$

$=14\times 14$

$=196c{m}^2$

Area of inner square JKLM having sides as follows:

$JK=LM=KL=JM=14-3-3-2=4cm$

Area of JKLM $=s\times s$

$=4\times 4$

$=16c{m}^2$

Area of semicircle $=\frac{\pi r^2}{2}$ {$d=4$cm $\therefore r=2cm$ }

$=\frac{3.14(2{)}^2}{2}$

$=6.28c{m}^2$

Area of $4$ semicircles $=6.28\times 4$

$=25.12c{m}^2$

Total unshaded Area = area of 4 semicircles + area of JKLM $=25.12+16$

$=41.12c{m}^2$

Shaded area $=$ Total square area$-$unshaded area

$=196c{m}^2-41.12c{m}^2$

$=154.88c{m}^2$.