Step-by-Step Solution:

To determine the perimeter of a geometric figure with a perimeter of 81 units, we need to consider the shape in question. Since the term "perimeter" typically refers to a two-dimensional figure, we'll assume it's a polygon.

1. Identify the Shape:

   Since the term "perimeter" is mentioned without specifying the shape, we can assume it refers to a polygon.

2. Understand the Perimeter Formula:

   • For a regular polygon, the perimeter ( P ) is given by: [ P = n \times s ] where:
     • ( n ) is the number of sides.
     • ( s ) is the length of each side.

3. Given Perimeter:

   ( P = 81 ) units.

4. Determine the Number of Sides:

   Without additional information about the number of sides, we can't determine the exact side length. However, if we assume the polygon is regular and has 81 sides, each side would be: [ s = \frac{P}{n} = \frac{81}{81} = 1 \text{ unit} ] Thus, the perimeter is 81 units.

5. Conclusion:

   • If the figure is a regular polygon with 81 sides, each side is 1 unit long, and the perimeter is 81 units.

[ \boxed{81} ]