In the given figure, AB and PQ are perpendicular diameters of the circle whose centre is O and radius OA = 7 cm. Find the area of the shade region.

Explanation

Diameter of the smaller circle `= OQ = OA = 7 cm`
Radius (r) `= (7)/(2) = 3.5 cm`
Area of the smaller circle `= pi r^(2)`
`= (22)/(7) xx (7)/(2) xx (7)/(2) cm^(2) = (77)/(2) cm^(2)`
`= 38.5 cm^(2)`
Area of the semicircle APBOA `= (1)/(2) pi r^(2)` (where, `r_(1) =` radius of semicle APBOA)
`= (1)/(2) xx (22)/(7) xx 7 xx 7 cm^(2) = 77 cm^(2)`
Area of `Delta APB = (1)/(2) xx AB xx OP = (1)/(2) xx 14 xx 7 = 49 cm^(2)`
Area of the shaded region APB
=Area of the semicircle `-` Area of `DeltaAPB`
`= 77 cm^(2) - 49 cm^(2) = 28 cm^(2)`
Now, total area of the shaded region
= Area of the smaller circle (shaded) `+` Area of the shaded region APB
`= 38.5 + 28 = 66.5 cm^(2)`