To find the perimeter of the given figure, we need to analyze its components. The figure consists of:

1. A rectangular part with dimensions $1.2 \, \text{m}$ height and $1.6 \, \text{m}$ width.
2. A semicircular part with a diameter of $1.6 \, \text{m}$, which is placed on top of the rectangle.
3. A slanted side (right side), which can be calculated using the Pythagorean theorem.

Step 1: Calculate the semicircle's circumference.

The formula for the circumference of a circle is: $C = 2\pi r$ Since this is a semicircle, its perimeter is half of the circle's circumference: $C_{\text{semicircle}} = \pi r = \pi \times \frac{1.6}{2} = 0.8\pi \, \text{m}$

Step 2: Find the slanted side.

To find the length of the slanted side (right side of the figure), we use the Pythagorean theorem. The difference between the total base (2.5 m) and the rectangle's width (1.6 m) gives the horizontal leg of the right triangle: $\text{Horizontal leg} = 2.5 - 1.6 = 0.9 \, \text{m}$ The vertical leg is 1.2 m, so the slanted side is: $\text{Slanted side} = \sqrt{(1.2^2 + 0.9^2)} = \sqrt{1.44 + 0.81} = \sqrt{2.25} = 1.5 \, \text{m}$

Step 3: Add all sides to find the perimeter.

The perimeter consists of:

• The width of the rectangle (1.6 m),
• The height of the rectangle (1.2 m),
• The semicircle's arc ($0.8\pi$ m),
• The slanted side (1.5 m),
• The base (2.5 m).

The perimeter is: $\text{Perimeter} = 1.6 + 1.2 + 0.8\pi + 1.5 + 2.5$ Now, let's calculate the value: $\text{Perimeter} \approx 1.6 + 1.2 + 0.8 \times 3.1416 + 1.5 + 2.5$

I'll compute the exact value next.The perimeter of the given figure is approximately $9.31 \, \text{m}$.

Would you like more details or further clarifications?

Here are 5 related questions to explore:

1. How would the perimeter change if the semicircle's diameter were increased?
2. What is the area of the figure?
3. How can we derive the area of the semicircular section?
4. If the figure were three-dimensional (a cylinder with a similar base), how would we calculate the volume?
5. What is the relation between the perimeter and area for this shape?

Tip: Remember that the Pythagorean theorem is a powerful tool for finding distances in right triangles, which often appear in geometric figures.