Question

find the area of shaded region

Answer 1

Let sides of inner square  =  x  , So diameter of semicircle  =  x , And radius of semicircle  = 
So,

3 +  + x  +  +  3  =  14  

2x  = 14  -  6 

2x  =  8

x  =  4 cm 

So, 
Sides of inner square  =  4 cm 
And 
Radius of semicircle  =  2 cm 
So,

Area of shaded region  =  Area of inner square  +  4 ( Area of semicircle ) 
We know 
Area of square  = ( Side )2 
So, 
Area of inner square  =  42 =  16 cm2 
And 
We know Area of Semicircle  = 
So,
Area of semicircle  = 
So,
Area of shaded region  =  16  +  4 ( 6.2857 ) =  16 + 25.1428  =  41.1428  cm2                                      ( Ans )