To determine the perimeter of the quadrilateral, we need to sum all the side lengths. In the image provided, we have the following sides:

1. $9.3 \, \text{cm}$
2. $11.2 \, \text{cm}$
3. $8.7 \, \text{cm}$
4. The fourth side is missing and needs to be calculated using the given information.

Steps to solve:

1. The triangle formed by the 9.3 cm, 11.2 cm, and the missing side has a right angle. Using the Pythagorean theorem: $\text{missing side} = \sqrt{(11.2)^2 - (9.3)^2}$
2. Compute the length of the missing side.
3. Add all the side lengths together.

Calculation:

$\text{missing side} = \sqrt{(11.2)^2 - (9.3)^2}$ $\text{missing side} = \sqrt{125.44 - 86.49}$ $\text{missing side} = \sqrt{38.95} \approx 6.24 \, \text{cm}$

Now, sum all the sides: $\text{Perimeter} = 9.3 + 11.2 + 8.7 + 6.24 \approx 35.44 \, \text{cm}$

Final Answer:

$\boxed{35}$

Let me know if you have questions or would like a more detailed explanation!

Follow-up Questions:

1. What is the Pythagorean theorem, and how is it applied to triangles?
2. Can the missing side be calculated without the right angle information?
3. Why is rounding important when presenting final answers?
4. How does the 91° angle affect the calculations?
5. Could this problem be solved using trigonometry instead?

Tip:

Always double-check the rounding instructions in a question to ensure accuracy.