# Please solve sorry for what i hav written in paper

Dear Student,

Given :  Diameter of three small semicircle = 3 cm , So radius =  1.5 cm

And

Diameter of circle =  4.5 cm , So radius of circle  = 2.25 cm

And

Radius of big semicircle =  4.5 cm

Then,

Area of shaded region =  Area of big semicircle + Area of small semicircle  - Area of  circle - 2 ( Area of small semicircle )

We know area of circle = $\mathrm{\pi }$ r2 , So

Area of given circle  = $\mathrm{\pi }$ ( 2.25 )2  = 5.0625 $\mathrm{\pi }$ cm2

And we know area of semicircle = $\frac{1}{2}×$ $\mathrm{\pi }$ r2 , So

Area of big semicircle  = $\frac{1}{2}×$$\mathrm{\pi }$ ( 4.5 )2  = $\frac{1}{2}×$ 20.25 $\mathrm{\pi }$  = 10.125 $\mathrm{\pi }$ cm2

And

Area of small semicircle  = $\frac{1}{2}×$$\mathrm{\pi }$ ( 1.5 )2  = $\frac{1}{2}×$ 2.25 $\mathrm{\pi }$  = 1.125 $\mathrm{\pi }$ cm2

Therefore,
Area of shaded region = 10.125 $\mathrm{\pi }$ + 1.125 $\mathrm{\pi }$  - 5.0625 $\mathrm{\pi }$ - 2 ( 1.125 $\mathrm{\pi }$ ) = 10.125 $\mathrm{\pi }$ + 1.125 $\mathrm{\pi }$  - 5.0625 $\mathrm{\pi }$ - 2.25 $\mathrm{\pi }$ = 3.9375 $\mathrm{\pi }$ = 3.9375  = 12.375 cm2                                       ( Ans )