To solve the problem and find the perimeter of the given figure, let's break it down step by step:

Step 1: Analyze the figure

The figure consists of:

1. A straight horizontal segment of 9 cm.
2. Two vertical sides of 2 cm each.
3. A semi-circular curve at the bottom with a radius of 2 cm.
4. A triangular cutout with a base of 4 cm and a vertical height of 2 cm.
5. A horizontal segment of 3 cm within the triangular cutout.

Step 2: Calculate the curved length (semi-circle perimeter)

The semi-circle's perimeter is half the circumference of a full circle. Using the formula $C = \pi \cdot d$, and given the radius $r = 2$ cm (so $d = 4$ cm) and $\pi = 3$, $\text{Semi-circle length} = \frac{1}{2} \cdot \pi \cdot d = \frac{1}{2} \cdot 3 \cdot 4 = 6 \, \text{cm}.$

Step 3: Add all the line segments

The total length of the perimeter is: $9 \, \text{cm (top horizontal)} + 2 \, \text{cm (right vertical)} + 6 \, \text{cm (semi-circle)} + 2 \, \text{cm (left vertical)}.$

Since the triangle's 4 cm base is not part of the perimeter due to the cutout, it is excluded.

$\text{Perimeter} = 9 + 2 + 6 + 2 = 19 \, \text{cm}.$

Final Answer:

The perimeter of the figure is 19 cm.

Do you need further clarification, or have any questions about this calculation?

Follow-Up Questions:

1. Why does the triangle’s base not contribute to the perimeter?
2. How would the calculation change if the radius of the semi-circle were doubled?
3. Can we generalize this formula for figures with multiple semi-circles?
4. Why is $\pi = 3$ used instead of the more precise value $3.14$?
5. How does the triangular cutout affect the calculation?

Tip:

When dealing with composite shapes, break them into smaller, manageable parts and calculate each component separately!