To find the approximate area of the circle, we need to follow these steps:
1. Identify the given information:
- The circle is divided into 16 identical sectors.
- The base of one sector (which can be seen as the base of a triangle) is 1.56 units.
- The height of one sector (the height of the corresponding triangle) is 3.92 units.
2. Calculate the area of one sector:
- Each sector can be approximated as a triangle with a base of 1.56 units and a height of 3.92 units.
- The formula for the area of a triangle is [tex]\( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \)[/tex].
Plugging in the values:
[tex]\[
\text{Area of one sector} = \frac{1}{2} \times 1.56 \times 3.92
\][/tex]
Performing the multiplication and division:
[tex]\[
\text{Area of one sector} \approx 3.0576 \text{ square units}
\][/tex]
3. Calculate the total area of the circle:
- Since the circle is divided into 16 congruent sectors, the total area of the circle is 16 times the area of one sector.
[tex]\[
\text{Area of the circle} = 16 \times 3.0576
\][/tex]
Performing the multiplication:
[tex]\[
\text{Area of the circle} \approx 48.9216 \text{ square units}
\][/tex]
4. Match the calculated area with the given options:
- The option closest to our calculated value is [tex]\( 48.92 \)[/tex] units[tex]\(^2\)[/tex].
Thus, the approximate area of the circle is:
[tex]\[
\boxed{48.92 \text{ units}^2}
\][/tex]
