A sprinkler sprays water in a circular region with a radius of \(5 \text{ m}\). It is positioned in such a way that some of the water is landing on a nearby sidewalk.
In the diagram, the circle with centre \(O\) represents the circular region covered by the water sprinkler. Points \(A\) and \(B\) lie on the circle with \(\angle AOB=90\degree\) and \(OA = 5 \text{ m}\). The shaded region, which is the region inside sector \(AOB\) but outside of \(\triangle AOB\), represents the region of the sidewalk where water is landing.
Determine the area of the region of the sidewalk where the water is landing, correct to one decimal place.
Theme: Geometry & Measurement