To solve the problem, we need to calculate the perimeter of $P'Q'R'S'T'U'$, the dilated image of $PQRSTU$ with a scale factor of 0.8 centered at point $S$.

Step 1: Measure the original lengths of the sides of $PQRSTU$.

From the graph:

• $PQ$ and $RU$ have lengths of 6 units each.
• $PS$ and $QT$ have lengths of 4 units each.
• $ST$ and $TU$ have lengths of 5 units each.

Step 2: Scale these lengths by the scale factor.

Each length is multiplied by the scale factor of 0.8:

• $P'Q'$ and $R'U'$: $6 \times 0.8 = 4.8$ units.
• $P'S'$ and $Q'T'$: $4 \times 0.8 = 3.2$ units.
• $S'T'$ and $T'U'$: $5 \times 0.8 = 4$ units.

Step 3: Calculate the perimeter of $P'Q'R'S'T'U'$.

The perimeter is the sum of all side lengths: $\text{Perimeter} = 2(P'Q' + P'S' + S'T') = 2(4.8 + 3.2 + 4) = 2 \times 12 = 24 \, \text{units}.$

Final Answer:

The perimeter of $P'Q'R'S'T'U'$ is 24 units.

Would you like more detailed steps or help with related topics? Here are five follow-up questions you might consider:

1. How do you determine the center of dilation on a graph?
2. What happens to angles during dilation? Do they change?
3. Can you describe a situation where a scale factor is greater than 1? What would happen?
4. How does dilation affect the area of a polygon compared to its perimeter?
5. Can you explain the difference between dilation and translation in transformations?

Tip: Always verify lengths on a graph carefully to ensure accurate calculations, especially with scaled figures.