pls solve it widout giving any link

In the given figure, ABCD is a rectangle of dimensions 21 cm x 14 cm. A 
semicircle is drawn with BC as diameter. Find the area and the 
perimeter of the shaded region in the figure. 
 

Dear Student,

Please find below the solution to the asked query:

As given : A semicircle is drawn with diameter BC   and given ABCD is a rectangle , so AD  =  BC  =  14 cm ( Opposite sides are equal in rectangle ) , Then

Radius of given semicircle  = 7 cm

Area of shaded region  =  Area of rectangle -  Area of semicircle

We know area of rectangle =  Length $\times$ Breadth  and Area of semicircle = $\frac{\mathrm{\pi }\mathit{ }{r}^2}{2}$ , So

Area of shaded region  = 21 $\times$ 14  - $\frac{{\displaystyle \frac{22}{7}}{\displaystyle \times }\mathit{ }{7}^2}{2} = 294 - \frac{22 \times 7}{2}= 294 - 11 \times 7= 294 - 77 =\mathbf{217}\mathbf{ }{\mathbf{cm}}^{\mathbf{2}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$

We know circumference of semicircle ( excluding diameter ) = $\mathrm{\pi } r$ , So

Circumference of given semicircle ( excluding diameter ) =$\frac{22}{7}\times 7$ = 22 cm

Then,

Perimeter of given shaded region = AB  + AD + CD +  Circumference of given semicircle , Substitute all values we get :


Perimeter of given shaded region = 21 + 14 + 21 + 22 = 78 cm                                     ( Ans )


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