The shape below consists of a semi-circle and a rectangle Use Π = 3, 14 Determine the perimeter of the combined shape above

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.

Learn how to calculate the perimeter of a combined shape consisting of a semi-circle and a rectangle using π = 3.14. Includes step-by-step calculations and formulas for the perimeter of both the semi-circle and rectangle. Suitable for Grades 7-9 students.

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