Question

Find the area of the shaded region, thank you!

Answer 1

5.1 cm² (nearest tenth)

Explanation:

`\mathsf{area\ of \ sector=(\theta\pi r^2)/(360) \ (where\ \theta \ is \ measured \ in \ degrees)}`

Given:

• r = 5
• 
  `\theta` = 80°

`\implies \mathsf{area\ of \ sector=(80 \cdot\pi\cdot 5^2)/(360)=(50)/(9)\pi \ cm^2}`

`\mathsf{area\ of \ triangle=\frac12 ab\sin C}`

Given:

• a = 5
• b = 5
• C = 80°

`\implies \mathsf{area\ of \ triangle=\frac12 \cdot 5 \cdot 5\sin (80)=(25)/(2)\sin(80) \ cm^2}`

Area of shaded area = area of sector - area of triangle

`\implies \mathsf{area=(50)/(9)\pi-(25)/(2)\sin(80)}`

Therefore, area = 5.1 cm² (nearest tenth)