[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{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
Solution in the attachment
[tex]→Circle ⟹ π × r2 r [/tex]
[tex]→Triangle \: ⟹ ½ × b × h [/tex]
[tex]→Square ⟹ a² [/tex]
[tex]→Rectangle ⟹ l × w [/tex]
[tex]→Parallelogram ⟹ b × h [/tex]
[tex]→Trapezium ⟹ ½(a+b) × h[/tex]
[tex]→Ellipse ⟹ πab[/tex]
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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
Solution in the attachment
★More information
[tex]→Circle ⟹ π × r2 r [/tex]
[tex]→Triangle \: ⟹ ½ × b × h [/tex]
[tex]→Square ⟹ a² [/tex]
[tex]→Rectangle ⟹ l × w [/tex]
[tex]→Parallelogram ⟹ b × h [/tex]
[tex]→Trapezium ⟹ ½(a+b) × h[/tex]
[tex]→Ellipse ⟹ πab[/tex]