Question

In figure, $AB$ and $CD$ are two perpendicular diameters of a circle with centre $O$. If $OA=7cm$, find the area of the shaded region. [Take π=22/7]

Answer 1

Radius of big circle $=OA=7cm$.
$AB=14cm$ and $\angle CBD=90°$
Area of big circle$=\pi r^2=\pi \times 7\times 7=49\pi c{m}^2$.
Similarly,
Area of circle with diameter $AO=\pi r^2=\pi \times \frac{7}{2}\times \frac{7}{2}=\frac{49\pi }{4}c{m}^2$.

Area of triangle $BCD=\frac{1}{2}\times (CD\times OB)=\frac{1}{2}(14\times 7)=49c{m}^2$.

Area of shaded region = Area of big circle - Area of circle with diameter $AO$ - Area of triangle $BCD$
Area of shaded region = $49\pi c{m}^2$$-$$\frac{49\pi }{4}c{m}^2-49c{m}^2=66.5c{m}^2$.