To determine the perimeter of the combined shape (a semi-circle and a rectangle), let's outline the steps:

1. Identify the components of the shape:

   • The semi-circle has a diameter equal to the width of the rectangle.
   • The rectangle has a width equal to the diameter of the semi-circle and a given height.

2. Define variables:

   • Let $d$ be the diameter of the semi-circle (which is also the width of the rectangle).
   • Let $h$ be the height of the rectangle.

3. Calculate the perimeter:

   • The perimeter of the semi-circle is half the circumference of a full circle plus the diameter: $\text{Perimeter of semi-circle} = \frac{1}{2} \times \pi \times d + d = \frac{1}{2} \times 3.14 \times d + d$
   • The perimeter of the rectangle (excluding the side that coincides with the diameter of the semi-circle) is: $\text{Perimeter of rectangle (excluding top width)} = 2 \times h$
   • Combine the perimeters: $\text{Total perimeter} = \left(\frac{1}{2} \times 3.14 \times d + d\right) + 2 \times h$

4. Simplify the equation: $\text{Total perimeter} = \left(1.57 \times d + d\right) + 2 \times h = 2.57 \times d + 2 \times h$

If the values of $d$ and $h$ are known, you can plug them in to find the exact perimeter.

Would you like to proceed with specific values for $d$ and $h$, or do you have any other questions?

Here are five related questions to explore further:

1. How would the perimeter change if the diameter of the semi-circle was doubled?
2. What would be the area of the combined shape?
3. How does the perimeter change if the shape was a full circle instead of a semi-circle?
4. How do you calculate the perimeter of irregular shapes?
5. How can the formula be adapted if the shape had more than one semi-circle?

Tip: For combined shapes, break down the perimeter calculation into manageable parts, considering both straight and curved segments separately.