The shaded part of the circle is the larger sector:
[tex]\begin{gathered} \text{The angle subtended by the larger sector by the center is} \\ 360^0-60^0=300^0\text{ (sum of angles at a point is 360 degr}ees) \end{gathered}[/tex]
The area of a sector is given by the formula:
[tex]\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ \theta=300^0 \\ r=x \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} A=\frac{300}{360}\times\pi x^2 \\ =\frac{5}{6}\pi x^2 \end{gathered}[/tex]
