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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.

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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