In order to find the area of the sector, let's consider the formula for the area of a circle:
[tex]A=\pi r^2[/tex]The complete circle is equivalent to a sector with central angle 2pi. Knowing this, we can write the following rule of three:
[tex]\begin{gathered} central\text{ }angle\rightarrow area \\ 2\pi\rightarrow\pi r^2 \\ \pi\rightarrow x \end{gathered}[/tex]Now, we can write the following proportion and solve it for x:
[tex]\begin{gathered} \frac{2\pi}{\pi}=\frac{\pi r^2}{x}\\ \\ 2x=\pi r^2\\ \\ x=\frac{\pi r^2}{2}=\frac{\pi\cdot0.7^2}{2}=0.77\text{ in^^b2} \end{gathered}[/tex]Therefore the area is 0.77 in².
