[tex]A=\frac{98\pi}{15}in^{2}[/tex]
1) Let's sketch this out to better get it:
2) Note that the area of that sector can be found by making use of the following formula, considering that the unit is radians we can write:
[tex]\begin{gathered} A=\frac{1}{2}\cdot r^2\cdot\alpha \\ A=\frac{1}{2}\cdot(7)^2\cdot\frac{4\pi}{15} \\ A=\frac{49}{2}\cdot\frac{4\pi}{15} \\ A=\frac{98\pi}{15}in^{2} \end{gathered}[/tex]
As it is in radians, we use this formula. If it was in degrees we'd use another formula slightly different.
