Identify the correct statement.

The correct option is: The shape of figure determines the perimeter.

Let us analyze each statement step-by-step to determine its correctness:

1. "If two figures have same area, their perimeters are equal."
This statement is incorrect. Two figures can have the exact same area but different perimeters. For instance, consider a rectangle of dimensions 4 cm × 9 cm (Area = 36 cm², Perimeter = 26 cm) and a square of side 6 cm (Area = 36 cm², Perimeter = 24 cm).

2. "If two figures have same perimeter, their areas are equal."
This statement is also incorrect. Two figures can have the same perimeter but enclose different areas. For example, a rectangle of dimensions 2 cm × 6 cm has a perimeter of 16 cm and an area of 12 cm², whereas a square of side 4 cm has the same perimeter of 16 cm but a larger area of 16 cm².

3. "The units of perimeter and area are same."
This statement is incorrect. Perimeter measures the total continuous length of the boundary of a figure, so its unit is a linear unit (e.g., cm, m). Area measures the amount of surface enclosed by a boundary, so its unit is a square unit (e.g., cm², m²).

4. "The shape of figure determines the perimeter."
This statement is correct. The specific shape of a closed figure defines its boundary structure and determines the length of all its outer sides, thereby directly determining its perimeter.