Answer:
[tex]A\approx54.80\text{ m}^2[/tex]
Step-by-step explanation:
The area of a sector of a circle is given by the equation:
[tex]A=\dfrac{\theta}{360\°} \cdot \pi r^2[/tex]
We can identify two parts of this equation:
- area of the whole circle ([tex]\pi r^2[/tex])
- the fraction of the whole circle's area that the sector takes up ([tex]\theta / 360\°[/tex])
Plugging in the given values, we get:
[tex]A=\dfrac{89\°}{360\°} \cdot \pi (8.4\text{ m})^2[/tex]
[tex]\boxed{A\approx54.80\text{ m}^2}[/tex]
