To find the area of sector MNP in circle N, we can use the formula for the area of a sector, which is given by:
\[ \text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where \(\theta\) is the angle of the sector in degrees and \(r\) is the radius of the circle.
In this case, we have:
- \(\theta = 124^\circ\)
- The distance \(MN = 13\) can be interpreted as the radius \(r\) of the circle.
Now, substitute the known values into the formula:
\[ \text{Area of Sector} = \frac{124}{360} \times \pi \times 13^2 \]
Calculating \(13^2\):
\[ 13^2 = 169 \]
Now substituting that back into the formula:
\[ \text{Area of Sector} = \frac{124}{360} \times \pi \times 169 \]
First, simplify \(\frac{124}{360}\):
\[ \frac{124}{360} = \frac{31}{90} \quad \text{(dividing both by 4)} \]
Now the area becomes:
\[ \text{Area of Sector} = \frac{31}{90} \times \pi \times 169 \]
Now, calculate the numerical value:
\[ \text{Area of Sector} \approx \frac{31}{90} \times 3.14159 \times 169 \]
First calculate \(\frac{31}{90} \times 169\):
\[ \frac{31 \times 169}{90} \approx \frac{5239}{90} \approx 58.7667 \]
Now multiply by \(\pi\):
\[ \text{Area of Sector} \approx 58.7667 \times 3.14159 \approx 184.629 \]
Rounding to the nearest hundredth:
\[ \text{Area of Sector} \approx 184.63 \]
Thus, the area of sector MNP is approximately \(\boxed{184.63}\).