Question

Find the area of the shaded region round to the nearest tenth

Answer 1

Answer: 818.4

Step-by-step explanation:

Using the area of a sector formula, we get the area of the entire sector is $(\pi)(27.8^{2})\left(\frac{150}{360} \right)$.

Using the formula $A=\frac{1}{2} ab \sin C$, we get the area of the triangle is $\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ})$.

So, the area of the shaded sector is $(\pi)(27.8^{2})\left(\frac{150}{360} \right)-\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ}) \approx \boxed{818.4}$