SOLUTION
The formula for area of segment is given to be
[tex]A=\frac{\theta}{360}\pi r^2-\frac{1}{2}r^2\sin \theta[/tex]
From the image
[tex]\theta=120^{\circ},r=4[/tex]
substituting these values gives
[tex]A=\frac{120}{360}\times\pi(4)^2-\frac{1}{2}(4)^2\sin 120[/tex]
Solve for A
[tex]\begin{gathered} A=\frac{1}{3}\times\pi\times16^{}-\frac{1}{2}\times16\times^{}0.8660 \\ A=16.76-6.93 \\ A=9.83 \end{gathered}[/tex]
Therefore, the area of the shaded segment is 9.83 square meters
