Question

In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
$[Use\pi =\frac{22}{7}]$

Answer 1

AB and CD are the diameters of a circle with centre O.
Therefore, OA = OB = OC = OD = 7 cm (Radius of the circle)
= Area of the circle with diameter OB + (Area of the semi-circle ACDA - Area of $\Delta$ ACD)
$=\pi (\frac{7}{2}{)}^2+(\frac{1}{2}\times \pi \times (7{)}^2-\frac{1}{2}\times 14cm\times 7cm)=\frac{22}{7}\times \frac{49}{4}c{m}^2+\frac{1}{2}\times \frac{22}{7}\times 49c{m}^2-\frac{1}{2}\times 14cm\times 7cm=\frac{77}{2}c{m}^2+77c{m}^2-49c{m}^2=66.5c{m}^2$
Thus, the area of the shaded region is $66.5c{m}^2.$