Identify the correct statement.

Correct Answer: The shape of figure determines the perimeter.

Step-by-step Explanation:

Let us analyze each statement one by one to determine which one is correct:

1. Statement 1: "If two figures have same area, their perimeters are equal."
This statement is false. For example, consider a rectangle of sides 2 units and 8 units. Its area is:
$\text{Area}=2\times 8=16\text{square units}$
Its perimeter is:
$\text{Perimeter}=2\times (2+8)=20\text{units}$
Now, consider a square with side 4 units. Its area is:
$\text{Area}=4\times 4=16\text{square units}$
Its perimeter is:
$\text{Perimeter}=4\times 4=16\text{units}$
Both figures have the same area (16 square units), but their perimeters are different (20 units vs 16 units).

2. Statement 2: "If two figures have same perimeter, their areas are equal."
This statement is also false. For example, consider a rectangle of sides 1 unit and 5 units. Its perimeter is:
$\text{Perimeter}=2\times (1+5)=12\text{units}$
Its area is:
$\text{Area}=1\times 5=5\text{square units}$
Now consider a square with side 3 units. Its perimeter is:
$\text{Perimeter}=4\times 3=12\text{units}$
Its area is:
$\text{Area}=3\times 3=9\text{square units}$
Both figures have the exact same perimeter (12 units), but their areas are different (5 square units vs 9 square units).

3. Statement 3: "The units of perimeter and area are same."
This statement is false. Perimeter measures linear distance along the boundary (expressed in units like meters, centimeters, inches), while area measures the total surface covered (expressed in square units like square meters, square centimeters, square inches).

4. Statement 4: "The shape of figure determines the perimeter."
This statement is correct. The specific geometric shape of a figure dictates the formula and manner in which its perimeter (boundary length) is calculated (e.g., perimeter of a circle is $2\pi r$, perimeter of a square is $4s$, and perimeter of a triangle is the sum of its three side lengths).