Perimeter refers to the total distance around the boundary of a two-dimensional shape. It is calculated by adding up the lengths of all the sides of the shape. The concept of perimeter is essential in geometry as it helps us understand the length of the boundary of a shape.

Figures with the same perimeter can indeed have different areas. Let's explore this further.

Perimeter:
- The perimeter of a shape is the sum of the lengths of all its sides.
- It is measured in units such as centimeters, inches, or meters.
- Perimeter is a measure of the distance around the shape.

Area:
- The area of a shape is the measure of the space enclosed by the shape.
- It is measured in square units such as square centimeters, square inches, or square meters.
- Area is a measure of the surface covered by the shape.

Example:
Consider two rectangles with the same perimeter but different areas. Let's call them Rectangle A and Rectangle B.

Rectangle A:
- Length = 6 units
- Width = 2 units

Rectangle B:
- Length = 4 units
- Width = 4 units

Both rectangles have a perimeter of 16 units because the sum of all their sides is equal. However, their areas are different.

- Area of Rectangle A = Length x Width = 6 units x 2 units = 12 square units
- Area of Rectangle B = Length x Width = 4 units x 4 units = 16 square units

This example demonstrates that figures with the same perimeter can have different areas. The area of a shape depends not only on the length of its sides but also on the arrangement of those sides.

Explanation:
When the perimeter of a shape is fixed, there are countless ways to arrange its sides to form different shapes. Some arrangements may result in shapes with larger areas, while others may have smaller areas. The area is influenced by factors such as the length and width of the shape or the angles between its sides.

For example, a rectangle with a perimeter of 20 units can have various dimensions:
- Length = 8 units, Width = 2 units → Area = 16 square units
- Length = 6 units, Width = 4 units → Area = 24 square units
- Length = 5 units, Width = 5 units → Area = 25 square units

In each case, the perimeter remains the same, but the areas differ due to the different arrangements of the sides.

Conclusion:
In conclusion, figures with the same perimeter can have different areas. The area of a shape not only depends on the length of its sides but also on their arrangement. Understanding the relationship between perimeter and area helps in analyzing and comparing shapes in geometry.

The boundary of an object is called perimeter