The area of the composite figure is 29.92 m².
Area of Compound Shapes
This exercise requires your knowledge about the area of compound shapes. For solving this, you should:
- Identify the basic shapes;
- Calculate your individual areas;
- Sum each area found.
For finding the area, the steps are presented below.
- STEP 1 - Identify the basic shapes.
The figure of the question as informed is composed for a sector of circle and a rectangle. Therefore, you should sum the area of these geometric figures.
- STEP 2 - Find the area of the sector of circle.
Area of the sector of circle= [tex]\frac{\theta \cdot \pi }{360}\cdot r^2[/tex], where:
r= 5.5 m
Θ=30°
Then,
[tex]\frac{\theta \cdot \pi }{360}\cdot r^2\\ \\ \frac{\;30\cdot \pi }{360}\cdot 5.5^2=7.92 m^2[/tex]
- STEP 3 - Find the area of the rectangle.
Area of the rectangle=[tex]b*h[/tex] . The figure shows:
b= length of the base= 5.5 m
h=height= 4 m
Thus, the area of the rectangle=[tex]5.5*4=22m^2[/tex] .
- STEP 4 - Find the composite figure
[tex]A_{composite\; figure}=A_{sector\; circle}+A_{rectangle}\\ \\ A_{composite\; figure}=7.92+22=29.92\; m^2[/tex]
Learn more about the area of compound shapes here:
brainly.com/question/15884960
