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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.

This composite figure is created by placing a sector of a circle on a rectangle. What-example-1
User Vyctorya
by
8.5k points

2 Answers

4 votes

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

User Anthony Forloney
by
7.1k points
3 votes

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}=(\theta\pi r^2)/(360) \textsf{ (when } \theta \textsf{ is measured in degrees)}


=(30 \cdot\pi\cdot5.5^2)/(360)


=(121)/(48)\pi \textsf{ m}^2

Total area

total area = area of rectangle + area of sector


=22 +(121)/(48)\pi

= 29.91943148...

= 29.9 m² (nearest tenth)

User Zach Weg
by
8.5k points

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