Final answer:
The perimeter of a polygon cannot be determined without knowing the lengths of all its sides. For predefined shapes such as rectangles, the formula P = 2l + 2w can be used, where l is the length and w is the width. Vector addition principles are employed for irregular shapes to ascertain the missing dimensions.
Step-by-step explanation:
To find the perimeter of a polygon given that ZB = ZD, all we need are the lengths of the sides of the polygon. Unfortunately, without the specific measurements of each side, we cannot calculate the perimeter accurately. In the context of the examples provided in the question fragments, the town square has a perimeter calculated by P = 2l + 2w (where l is the length and w is the width), hence for the square with dimensions 39.2 meters by 17.5 meters, its perimeter would be 2(39.2) + 2(17.5) = 113.4 meters.
In the case of the farmer's four-sided plot or the new landowner's triangular plot, you need to know all relevant lengths and use vector addition principles to calculate the missing side before determining the total perimeter.