Unit Hydrograph and its Characteristics:
A unit hydrograph is a graphical representation of the runoff response of a watershed to a unit amount of rainfall over a specific duration. It helps in estimating the peak discharge and hydrograph shape for a given storm event. The characteristics of a unit hydrograph include its shape, duration, and peak discharge.

Triangular Shape and Base Period:
In this case, the unit hydrograph for the watershed is triangular in shape. The triangular shape implies that the rising limb and falling limb of the hydrograph have the same slope. The base period of the unit hydrograph is given as 20 hours, which means that the hydrograph represents the runoff response for a 20-hour storm event.

Area of the Watershed:
The area of the watershed is given as 500 hectares. The area of a watershed is an important parameter in hydrological calculations as it determines the volume of runoff generated during a storm event.

Calculating Peak Discharge:
To calculate the peak discharge in m3/h, we need to use the area and the base period of the unit hydrograph.

1. Convert the area from hectares to square meters:
- 1 hectare = 10,000 square meters
- Area of the watershed = 500 hectares = 500 * 10,000 square meters = 5,000,000 square meters.

2. Calculate the volume of runoff generated during the storm event:
- Volume = Area * Base Period
- Volume = 5,000,000 square meters * 20 hours

3. Convert the volume from cubic meters to cubic millimeters:
- 1 cubic meter = 1,000,000,000 cubic millimeters
- Volume = 5,000,000 square meters * 20 hours * 1,000,000,000 cubic millimeters/cubic meter

4. Calculate the peak discharge:
- Peak Discharge = Volume / Duration
- Peak Discharge = (5,000,000 square meters * 20 hours * 1,000,000,000 cubic millimeters/cubic meter) / (20 hours * 3600 seconds/hour)

5. Simplify the equation to obtain the peak discharge in m3/h:
- Peak Discharge = 5,000,000,000,000 cubic millimeters / 72,000 seconds
- Peak Discharge = 69,444,444.44 cubic millimeters/second
- Peak Discharge = 69,444.44 liters/second
- Peak Discharge = 69.44 m3/second
- Peak Discharge = 69.44 * 3600 m3/h
- Peak Discharge ≈ 250,000 m3/h

Therefore, the peak discharge in m3/h for the given watershed is approximately 250,000 m3/h, which is different from the correct answer of 5000. It seems there might be an error in the calculation or the given answer.