We know that Area of a sector of a circle = \[(1/2){{r}^{2}}\theta \],

Here  r is the radius and \[\theta \] is the angle in radians subtended by the arc at the center of the circle

From the given question, Radius of circle = \[28\] cm

Angle subtended at the center = \[{{45}^{\circ }}\]

Angle subtended at the center (in radians) = \[\theta \] \[45\pi /180\] = \[\pi /4\]

∴ Area of a sector of a circle = \[\frac{1}{2}{{r}^{2}}\theta \]

= \[\frac{1}{2}\times {{(28)}^{2}}\times (\pi /4)\]

= \[28\times 28\times (22/8\times 7)\]

= \[308\] \[c{{m}^{2}}\]

The area of a sector of a circle is \[308\] \[c{{m}^{2}}\]