There are 12 hourly division for the clock.

Angle per hour = $\frac{\mathrm{360°}}{12}$ = 30°

Angle of the sector of the hour hand swept = hours x 30°

The hours from 13:15 to 17:45 is 4.5 hours

Angle of the sector of the hour hand swept = 4.5 x 30° = 135°

The length of the hour hand is the radius of the circular clock.

Radius = 3.5

π = $\frac{22}{7}$

Area swept by the hour hand = $\frac{\mathrm{135°}}{360}$ x $\frac{22}{7}$ x 3.5 cm x 3.5 cm

Area swept by the hour hand = 14.4375 cm²

Area swept by the hour hand = 14.4 cm²(three significant figures)