To find the area of sector FGH in circle G, we need to use the formula for the area of a sector:
\[ \text{Area of sector} = \frac{m\angle \text{FGH}}{360^\circ} \times \pi r^2 \]
Where:
- \( m\angle FGH = 60^\circ \) (given)
- \( r = FG = 5 \) (given as the radius)
Now we can substitute the values into the formula.
- First, calculate \( \pi r^2 \):
\[ r = 5 \implies r^2 = 5^2 = 25 \]
\[ \pi r^2 = \pi \times 25 \approx 78.54 \quad (\text{using } \pi \approx 3.14) \]
- Now plug this into the area formula:
\[ \text{Area of sector} = \frac{60}{360} \times \pi r^2 = \frac{1}{6} \times 78.54 \]
- Calculate the fraction:
\[ \frac{1}{6} \times 78.54 \approx 13.09 \]
Therefore, the area of sector FGH, rounded to the nearest hundredth, is
\[ \boxed{13.09}. \]