Introduction:
In this problem, we are given the length and breadth of a field along with their respective accuracies. We need to calculate the percentage error in the area of the field.

Given:
Length of the field = 22.4 cm
Breadth of the field = 15.8 cm
Accuracy = 0.2 cm

Calculating the area:
The area of a rectangle is given by the formula: Area = Length * Breadth

Substituting the given values:
Area = 22.4 cm * 15.8 cm
Area = 353.92 cm^2

Calculating the maximum and minimum possible values for the length and breadth:
Since the measurements have been taken with an accuracy of 0.2 cm, the actual values of the length and breadth can vary within ±0.2 cm.

Maximum possible length = 22.4 cm + 0.2 cm = 22.6 cm
Minimum possible length = 22.4 cm - 0.2 cm = 22.2 cm

Maximum possible breadth = 15.8 cm + 0.2 cm = 16 cm
Minimum possible breadth = 15.8 cm - 0.2 cm = 15.6 cm

Calculating the maximum and minimum possible areas:
Using the maximum and minimum possible values for the length and breadth, we can calculate the maximum and minimum possible areas.

Maximum possible area = Maximum possible length * Maximum possible breadth
Maximum possible area = 22.6 cm * 16 cm
Maximum possible area = 361.6 cm^2

Minimum possible area = Minimum possible length * Minimum possible breadth
Minimum possible area = 22.2 cm * 15.6 cm
Minimum possible area = 346.32 cm^2

Calculating the percentage error in the area:
Percentage error in the area can be calculated using the formula:

Percentage error in the area = (|Maximum possible area - Minimum possible area| / Actual area) * 100

Substituting the values:
Percentage error in the area = (|361.6 cm^2 - 346.32 cm^2| / 353.92 cm^2) * 100
Percentage error in the area = (15.28 cm^2 / 353.92 cm^2) * 100
Percentage error in the area ≈ 4.32%

Conclusion:
The percentage error in the area of the field is approximately 4.32%. This means that the actual area of the field can vary by around 4.32% due to the measurement inaccuracies in the length and breadth.