Answer: 818.4
Step-by-step explanation:
Using the area of a sector formula, we get the area of the entire sector is [tex](\pi)(27.8^{2})\left(\frac{150}{360} \right)[/tex].
Using the formula [tex]A=\frac{1}{2} ab \sin C[/tex], we get the area of the triangle is [tex]\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ})[/tex].
So, the area of the shaded sector is [tex](\pi)(27.8^{2})\left(\frac{150}{360} \right)-\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ}) \approx \boxed{818.4}[/tex]
