Question

1. This composite figure is created by placing a sector of a circle on a rectangle. What is the area of this composite figure? Show you work.

Answer 1

Answer:

29.92 m² (nearest hundredth)

Step-by-step explanation:

$\textsf{Area of a sector}=\dfrac{\theta}{360\textdegree}\pi r^2$

$\implies \textsf{area}=\dfrac{30}{360\textdegree}\pi \cdot 5.5^2=\dfrac{121}{48}\pi \textsf{ m}^2$

Area of rectangle = width × length

⇒ area = 4 × 5.5 = 22 m²

Total area = area of sector + area of rectangle

⇒ total area = $\dfrac{121}{48}\pi +22$ = 29.91943148... = 29.92 m² (nearest hundredth)