Answer :
The circle has a radius of [tex]$5$[/tex], so its area is calculated by
[tex]$$
\text{Circle Area} = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5.
$$[/tex]
Since the arc length [tex]$\widehat{AB}$[/tex] represents [tex]$\frac{1}{4}$[/tex] of the entire circumference, the corresponding sector occupies [tex]$\frac{1}{4}$[/tex] of the whole circle. Therefore, the area of sector [tex]$AOB$[/tex] is
[tex]$$
\text{Sector Area} = \frac{1}{4} \times 78.5 = 19.625.
$$[/tex]
Rounded to one decimal place, the area is approximately [tex]$19.6$[/tex] square units.
Thus, the correct answer is [tex]$\boxed{19.6}$[/tex] square units.
[tex]$$
\text{Circle Area} = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5.
$$[/tex]
Since the arc length [tex]$\widehat{AB}$[/tex] represents [tex]$\frac{1}{4}$[/tex] of the entire circumference, the corresponding sector occupies [tex]$\frac{1}{4}$[/tex] of the whole circle. Therefore, the area of sector [tex]$AOB$[/tex] is
[tex]$$
\text{Sector Area} = \frac{1}{4} \times 78.5 = 19.625.
$$[/tex]
Rounded to one decimal place, the area is approximately [tex]$19.6$[/tex] square units.
Thus, the correct answer is [tex]$\boxed{19.6}$[/tex] square units.
