From the diagram provided, the line segment WZ represents the radius of the circle. That means,
R = 5.3
Also, note that
[tex]WZ=XZ=5.3[/tex]
Next, observe that the angle formed by arc VW at VZW lies on a straight line with angle 108. Therefore,
[tex]\begin{gathered} \angle VZW+108=180\text{ (angles on a straight line equals 180)} \\ \angle VZW=180-108 \\ \angle VZW=72 \end{gathered}[/tex]
Also, arc VW equals arc XY, since both arcs are subtended by the same angle. Angle VZW and angle XZY are vertically opposite angles. Therefore we now have;
[tex]\begin{gathered} \text{Area of a sector=}\frac{\theta}{360}\times\pi\times r^2 \\ \text{Area of a sector=}\frac{72}{360}\times3.14\times5.3^2 \\ \text{Area of a sector=}\frac{1}{5}\times3.14\times28.09 \\ \text{Area of a sector=}0.2\times3.14\times28.09 \\ \text{Area of a sector=17.64052} \end{gathered}[/tex]
Note that there are two similar shaded sectors. Therefore the area of the shaded sectors equals;
Area = 17.64052 x 2
Area = 35.28104
Area = 35.28 km squared (rounded to the nearest hundredth)
