Question

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

Answer 1

Let r be the radius of the circle.
Thus, we have:
$r=\frac{28}{2}\mathrm{cm}$
=14 cm
Now,
Area of the shaded region = (Area of the square ABCD) $-$ 4(Area of the sector where $r=14\mathrm{cm}\mathrm{and}\theta =90°$)
$$\begin{gathered} =\left|\left(28\times 28\right)-4\left(\frac{22}{7}\times 14\times 14\times \frac{90}{360}\right)\right|{\mathrm{cm}}^2 \\ =\left|784-4\left(154\right)\right|{\mathrm{cm}}^2 \\ =\left(784-616\right){\mathrm{cm}}^2 \\ =168{\mathrm{cm}}^2 \end{gathered}$$