Note:
The area of a circle with radius r is πr².
An entire circle has a central angle of 360°.
For the sector with radius = (3+4) = 7cm and a central angle of 120°, the area is
[tex]A_{1}= \frac{120}{360}*(49 \pi ) = \frac{49}{3} \pi \, cm^{2} [/tex]
For the sector with radius = 3 cm and a central angle of 120°. the area is
[tex]A_{2}= \frac{120}{360} *(9 \pi ) = 3 \pi \, cm^{2}[/tex]
The area of the shaded sector (see the figure) is
[tex]A=A_{1}-A_{2} = ( \frac{49}{3} -3) \pi = \frac{40}{3} \pi \, cm^{2} [/tex]
Answer: [tex] \frac{40}{3} \pi \, cm^{2}[/tex]
