Question

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In the figure, ABCD is a square of side 14 cm. Semi-circles are drawn with
each side of square as diameter. Find the area of the shaded region.

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Answer 1

Given :

ABCD is a square

side od square = 14cm

To Find : Area of shaded region

Construction : Let us mark the shaded region as I , II , III , IV

Solution :

First , let us find the area of square .

Side = 14 cm

Area of square ABCD :

$- > {(side)}^{2}$

$- > {(14)}^{2}$

$- > 196 {cm}^{2}$

Also ,

Diameter of semicircle = Side of square

Radius of semi-circle =

$- > \frac{side}{2}$

$- > \frac{14}{2}$

$- > 7 \: cm$

Area of semi circle AD =

$- > \frac{1}{2} \times \pi {r}^{2}$

$- > \frac{1}{2} \times \frac{22}{7} \times 7 \times 7$

$- > 11 \times 7$

$- > 77 {cm}^{2}$

Since radius is same for semi- circle AD , BC , AB and CD

Area of all semi - circle = 77 cm ^2

Now ,

Area of region I + Area of region III

--> Area of square ABCD - ( Area of semi-circle AD + Area of semicircle BC )

Area of region II + Area of region IV

--> Area of square ABCD - ( Area of semi-circle AB + Area of semicircle CD )

So ,

Area of region ( I + II + III + IV )

--> 2 ( Area of square ABCD ) - ( Area of semicircles AD + BC + AB + CD )

Putting the values :

--> 2(196) - ( 77 + 77 + 77 + 77 )

--> 200 - 4 × 77

--> 392 - 308

--> 84cm^2

Area of shaded region = 84 cm ^2

I hope it helps u dear friend ^_^♡♡

Answer 2

Step-by-step explanation:

Hope this helps you ✔️✔️