Answer:
5.1 cm² (nearest tenth)
Step-by-step explanation:
[tex]\mathsf{area\ of \ sector=\dfrac{\theta\pi r^2}{360} \ (where\ \theta \ is \ measured \ in \ degrees)}[/tex]
Given:
- r = 5
- [tex]\theta[/tex] = 80°
[tex]\implies \mathsf{area\ of \ sector=\dfrac{80 \cdot\pi\cdot 5^2}{360}=\dfrac{50}{9}\pi \ cm^2}[/tex]
[tex]\mathsf{area\ of \ triangle=\dfrac12 ab\sin C}[/tex]
Given:
[tex]\implies \mathsf{area\ of \ triangle=\dfrac12 \cdot 5 \cdot 5\sin (80)=\dfrac{25}{2}\sin(80) \ cm^2}[/tex]
Area of shaded area = area of sector - area of triangle
[tex]\implies \mathsf{area=\dfrac{50}{9}\pi-\dfrac{25}{2}\sin(80)}[/tex]
Therefore, area = 5.1 cm² (nearest tenth)
