https://file.aiquickdraw.com/mathbot/file/1727808656347wykylwth.jpg

The given image shows a polygon that appears to be a triangle inscribed around a circle. The lengths of two of its sides are given as 3 cm, and the third side is 9 cm. To find the perimeter of the polygon, we need to sum the lengths of all its sides.

### Steps to calculate the perimeter:
- The triangle has three sides:
  - Side \( AB = 3 \, \text{cm} \)
  - Side \( BC = 9 \, \text{cm} \)
  - Side \( AC = 3 \, \text{cm} \)

Since the polygon is a triangle and we are provided with all three side lengths, the perimeter \( P \) of the triangle is the sum of these sides:

\[
P = AB + BC + AC = 3 \, \text{cm} + 9 \, \text{cm} + 3 \, \text{cm} = 15 \, \text{cm}
\]

Thus, the perimeter of the polygon is:

\[
\boxed{15 \, \text{cm}}
\]

Would you like more details on how to solve similar problems, or do you have any other questions?

Here are 5 questions to explore this further:
1. How can we calculate the area of this triangle?
2. What is the significance of the inscribed circle in this triangle?
3. How do we find the radius of the circle inscribed in a triangle?
4. How can we determine if this triangle is isosceles or scalene?
5. What formula would be used to calculate the perimeter of other polygons?

**Tip**: In any polygon, the perimeter is simply the sum of the lengths of its sides, so knowing all side lengths makes the calculation straightforward!

Learn how to calculate the perimeter of a triangle with an inscribed circle, using the side lengths provided. This geometry problem focuses on understanding polygons and the simple formula to find the perimeter. Ideal for students in Grades 6-8.

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