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