Question

1. find the area of the sector and round to the nearest hundredths.

wy = 10.6 km
sector area = \boxed{} km²

Explanation:

Step1: Find circle radius

The length $WY = 10.6$ km is the diameter, so radius $r = \frac{10.6}{2} = 5.3$ km.

Step2: Calculate total circle area

Use circle area formula $A_{total} = \pi r^2$
$A_{total} = \pi (5.3)^2 = 28.09\pi$ km²

Step3: Find single shaded sector angle

Total circle is $360^\circ$, subtract the given $108^\circ$ and the equal white sector:
Angle of one shaded sector $\theta = \frac{360^\circ - 108^\circ - 108^\circ}{2} = 72^\circ$
Total shaded angle = $72^\circ \times 2 = 144^\circ$

Step4: Compute shaded sector area

Sector area = $\frac{\theta_{total}}{360^\circ} \times A_{total}$
$A_{sector} = \frac{144}{360} \times 28.09\pi = 0.4 \times 28.09\pi$
$A_{sector} = 11.236\pi \approx 11.236 \times 3.1416 \approx 35.30$

Answer:

$35.30$ km²