Answer :
First, we note that the radius is [tex]$r=5$[/tex], and we are given [tex]$\pi=3.14$[/tex]. The area of the entire circle is calculated by
[tex]$$
\text{Area} = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5.
$$[/tex]
Since the length of arc [tex]$\widehat{AB}$[/tex] is [tex]$\frac{1}{4}$[/tex] of the circumference, the area of sector [tex]$AOB$[/tex] is the same fraction of the circle's area. Therefore, the area of the sector is
[tex]$$
\text{Sector Area} = \frac{1}{4} \times 78.5 = 19.625.
$$[/tex]
Rounded to one decimal place, this value is [tex]$19.6$[/tex] square units.
Thus, the closest answer is:
A. 19.6 square units.
[tex]$$
\text{Area} = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5.
$$[/tex]
Since the length of arc [tex]$\widehat{AB}$[/tex] is [tex]$\frac{1}{4}$[/tex] of the circumference, the area of sector [tex]$AOB$[/tex] is the same fraction of the circle's area. Therefore, the area of the sector is
[tex]$$
\text{Sector Area} = \frac{1}{4} \times 78.5 = 19.625.
$$[/tex]
Rounded to one decimal place, this value is [tex]$19.6$[/tex] square units.
Thus, the closest answer is:
A. 19.6 square units.