In the given figure, ABCD is a square each of whose sides measures 28 cm.
Question:

In the given figure, ABCD is a square each of whose sides measures 28 cm. Find the area of the shaded region.

 

Solution:

Let r be the radius of the circle.
Thus, we have:

$r=\frac{28}{2} \mathrm{~cm}$

$=14 \mathrm{~cm}$

Now,

Area of the shaded region $=$ (Area of the square $A B C D$ ) $-4$ (Area of the sector where $r=14 \mathrm{~cm}$ and $\theta=90^{\circ}$ )

$=\left|(28 \times 28)-4\left(\frac{22}{7} \times 14 \times 14 \times \frac{90}{360}\right)\right| \mathrm{cm}^{2}$

$=|784-4(154)| \mathrm{cm}^{2}$

$=(784-616) \mathrm{cm}^{2}$

 

$=168 \mathrm{~cm}^{2}$

 

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