To find the area of the shaded sector of the circle, you can use the formula for the area of a sector:
\[ \text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle.
In this case, you have:
- \(\theta = 120^\circ\)
- \(r = 28 , \text{m}\)
Now, plug the values into the formula:
\[ \text{Area of sector} = \frac{120}{360} \times \pi \times (28)^2 \]
First, simplify \(\frac{120}{360}\):
\[ \frac{120}{360} = \frac{1}{3} \]
Now calculate \((28)^2\):
\[ (28)^2 = 784 \]
Now, plug that into the equation:
\[ \text{Area of sector} = \frac{1}{3} \times \pi \times 784 \]
Next, calculate \(\frac{784}{3}\):
\[ \frac{784}{3} \approx 261.33 \]
Now, multiply by \(\pi\):
\[ \text{Area of sector} \approx 261.33 \times \pi \approx 820.56 , \text{m}^2 , (\text{using} , \pi \approx 3.14) \]
Thus, the area of the shaded sector is approximately:
\[ \text{Area of sector} \approx 820.56 , \text{m}^2 \]
If you need the answer in terms of \(\pi\):
\[ \text{Area of sector} \approx \frac{784\pi}{3} , \text{m}^2 \]
So, the area of the shaded sector is:
\[ 261.33 , \text{m}^2 \text{ (approximately)}, \text{ or } \frac{784\pi}{3} , \text{m}^2 \text{ (exactly).} \]