Question

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

Answer 1

Answer:

area of the figure: 29.92 m²

formula's:

• area of rectangle: length * width

• area of sector: ∅/360 * πr²

solving steps:

area of rectangle + area of sector

5.5 * 4 + 30/360 * π(5.5)²

22 + 7.919

29.92 m²

Answer 2

Answer:

Calculate the area of the sector and the area of the rectangle separately, then add them together to determine the area of the composite figure.

Rectangle

Area of a rectangle = width × length

                                = 4 × 5.5

                                = 22 m²

Sector

$\textsf{area of sector}=\dfrac{\theta\pi r^2}{360} \textsf{ (when } \theta \textsf{ is measured in degrees)}$

                     $=\dfrac{30 \cdot\pi\cdot5.5^2}{360}$

                     $=\dfrac{121}{48}\pi \textsf{ m}^2$

Total area

total area = area of rectangle + area of sector

                $=22 +\dfrac{121}{48}\pi$

                = 29.91943148...

                = 29.9 m² (nearest tenth)