Verified answer

Solution:

[tex]{\sf{Radius \: of \: sector \: \: OBA (R) = 21 \: cm}}[/tex]

[tex]\sf{Radius \: of \: Sector \: \: ODC (R) = 7 \: cm \:} [/tex]

[tex]\sf{Sector \: Angle \: { \theta} \: = 30° \: } [/tex]

[tex]\sf{Area \: of \: bigger \: sector \: (OAB) \:} [/tex]

[tex]\sf{ = {\dfrac{\pi} {r}^{2} { \theta}{360} }} [/tex]

[tex]\sf{= {\dfrac{22}{7}} \times {\dfrac{21 \times 21 \times 30}{360}} {cm}^{2} }[/tex]

[tex]\sf{ = 115.5 {cm}^{2}}[/tex]

[tex] \sf{Area \: of \: smaller \: sector \: (ODC) } [/tex]

[tex]\sf{ = {\dfrac{\pi} {r}^{2} { \theta}{360} }} [/tex]

[tex]\sf{= {\dfrac{22}{7}} \times {\dfrac{7 \times 7 \times 30}{360}} {cm}^{2} }[/tex]

[tex]\sf{ = 12.83{cm}^{2}}[/tex]

[tex]\sf{Area \:of \:smaller\: sector\; ( ODC) = 12.83 cm²}[/tex]

[tex]\sf{Area \:of \:shaded\: region} [/tex]

[tex] \sf{ = Area \: of \: bigger \: sector \: - \: Area \: of \: smaller \: sector}[/tex]

[tex]\sf{( 115.5 - 12.83) cm² = 102.67 cm²}[/tex]

Hence, Area of shaded region= 102.67 cm²