Question

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. [CBSE 2014]

Answer 1

In right triangle ABC
AC² = AB² + BC²
= 8² +6²
= 64 + 36
= 100
∴ AC² = 100
⇒ AC = 10 cm
Now, Radius of circle(OA)$=\frac{1}{2}\mathrm{AC}=5\mathrm{cm}$
Area of the shaded region = Area of circle − Area of rectangle OABC
$$\begin{gathered} =\mathrm{\pi }{\left(\mathrm{OA}\right)}^2-\mathrm{AB}\times \mathrm{BC} \\ =\frac{22}{7}\times {\left(5\right)}^2-8\times 6 \\ =78.57-48 \\ =30.57{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area of the shaded region is 30.57 cm².