Explanation:
Radius of bigger circle $ \displaystyle {{{r}_{1}}}$​ = OA = 7
Radius of smaller circle $ \displaystyle {{{r}_{2}}}$ = $ \displaystyle \dfrac{{{{r}_{1}}}}{2}$ = $ \displaystyle \dfrac{7}{2}$​
Area of the bigger circle $ \displaystyle {{{C}_{1}}}$​ = $ \displaystyle {\pi r_{1}^{2}}$​
​= $ \displaystyle \dfrac{22}{7}$ ​× 7 × 7 = 154 $ \displaystyle \text{c}{{\text{m}}^{2}}$​
 Area of the semicircle ​= $ \displaystyle \dfrac{154}{2}$​$ \displaystyle \text{c}{{\text{m}}^{2}}$ = 77 $ \displaystyle \text{c}{{\text{m}}^{2}}$​
Area of the smaller circle $ \displaystyle {{{C}_{2}}}$ ​= $ \displaystyle {\pi r_{2}^{2}}$
​= $ \displaystyle \dfrac{22}{7}$​ × $ \displaystyle \dfrac{7}{2}$​ × $ \displaystyle \dfrac{7}{2}$​ = $ \displaystyle \dfrac{77}{2}$​ $ \displaystyle \text{c}{{\text{m}}^{2}}$​
Area of the unshaded triangle △ABC = $ \displaystyle \dfrac{1}{2}$​ × AB × OC
​= $ \displaystyle \dfrac{1}{2}$ × 14 × 7 = 49 $ \displaystyle \text{c}{{\text{m}}^{2}}$​
$\therefore$ Area of the shaded portion
$=$ Area of the smaller circle +(Area of semicircle – Area of the triangle $△\mathrm{ABC}$ )
​= $ \displaystyle \dfrac{77}{2}$ ​+ (77 − 49) = 66.5 $ \displaystyle \text{c}{{\text{m}}^{2}}$​
Hence the area of the shaded region $66.5.$